Solve using the Zero Factor Property?

I don’t think I’ve heard of that property. Is the goal to find the zeroes of the equation?

@cockswain Zero factor property: Set each factor equal to zero and solve for the variable.

Oh, I just looked it up, that is what it is. Find the zeroes of the factors. So in other words 2y+3=0 and y+2 = 0. So y=-2 or -3/2. See? If you graphed it (and used x for the variable), those would be the points where it intercepts the x-axis.

@cockswain Ok, so then what happens to the 5(2y+3)?

5 is a constant and can never equal zero, so can be ignored. That explanation may not give you the intuition, but that is how it works. So that factor still becomes y=-3/2. You could put a 5, 7, pi, 102 or whatever in front of the factor and still get the same answer. In other words, if you made it 10y+15=0, it still simplifies to -3/2. Get it?

@cockswain So, I don’t just ignore the 5, I ignore the entire term? In other words, every time I get a problem in the same format (a)(b)+c(a)=0 I just ignore everything after the + and only care about (a)(b)?

The final is tomorrow, so I’m not really concerned with getting it on a gut level, just knowing the tricks so I don’t fail

You started with:
(2y+3)(y+2)=-5(2y+3)

The (2y+3) is a multiplier of each side. So the first simplification is: divide each side of the equation by (2y+3).

This leaves you with
y+2 = -5

Surely you can solve that.

And now the book is saying the correct answer is -3/2, -7.

@CyanoticWasp But it’s the method that matters, and that isn’t zero factor.

Ah, yes, @CyanoticWasp is correct, sorry for the shitty advice. If you graph it, setting y = (2x +3)(x+2) and y=-5(2x+3) and see where they intersect, it is indeed where x =-1.5 and -7. I switched the variables, but the answer is the same. So if you just want the trick and you’re allowed a graphing calculator, that’s a sure way to solve.

And I’m honestly a tad puzzled about why the (2y +3) remains after it is cancelled, so I need to think for a bit. Maybe @CyanoticWasp can provide a quick explanation, otherwise I have about 20 min before I have to leave and I’m going to mull over it.

@cockswain I can do it other ways, it’s just that we don’t get the points unless we show our work, so if it says do it by a certain method and I do it another way, that’s one less point I get on the final.

Ah got it! FOIL the left side, multiply through the right side:
2y^2 + 7y + 6 = -10y – 15

2y^2 + 17y + 21 = 0

(2y + 3) (y + 7) = 0

Solving each factor, y = -3/2 and -7.

Whew. You won’t miss that point. Sorry for the confusion.

There is an easier way to do it.

(2y+3)(y+2)+5(2y+3)=0 <—(2y+3) is a common factor so…
(2y+3)(y+2+5)=0
(2y+3)(y+7)=0
Then do as you did.

(2y+3)(y+2)+5(2y+3)=0 == (2y+3)[(y+2)+5]=0 -> 2y+3=0 and (y+2)+5)=0

This is because if a product equals zero then at least one of the parts is, necessarily, zero.

@CyanoticWasp Do not divide both sides by 2y+3. It will cause you to lose a solution.

@roundsquare and @Thammuz have the right idea. Here is a little more detail if it helps:
Start with your original equation:
(2y+3)(y+2)=-5(2y+3)

Now, get everything on the same side so you can use the zero factor property.
(2y+3)(y+2)+5(2y+3)=0

Now you are going to factor. You already know how to do this. It’s the same thing as if I tell you 2x+2y=2(x+y). The 2 factors because it is the same in both terms. You are going to do the same thing, but instead of a 2, you have (2y+3) in both terms. So you get:
(2y+3)[(y+2)+5] = 0. Do you understand that step?

The next thing you want to do is simplify the part in the brackets:
(2y+3)(y+7)=0

Now you have two factors that equal zero when you multiply them. What do you know about zero? Zero times any number is zero. So if either 2y+3 is zero or y+7 is zero, the whole thing will be zero. That tells you that your possible solutions come from the equations:
2y+3=0
y+7=0

Solve each of these equations for y. You get:
y=-3/2
OR
y=-7
Either of these values will make the original equation true.

I hope that helps. Do you have any questions?

@bobbinhood Yes, yes I do. Will you take my final for me, please? XD

@papayalily I suspect I would enjoy that, but then you wouldn’t get the satisfaction of finishing what you started and knowing you had done your very best to earn your grade in the course. Besides, I have a few finals of my own that need my attention. :P Let us know how it goes.

@bobbinhood Exactly what is this satisfaction everyone keeps talking about? I never get any of that. I think it’s just a conspiracy to keep people doing their own shit…

@papayalily if you don’t get satisfaction out of it then why the fuck are you going to school?

@Thammuz Because I need my degree in order to become an architect. But I get the feeling that in your book I’ve just said something horribly, horribly wrong…

@papayalily You said architect. ;) (I’m an aspiring engineer, we don’t take kindly to your kind)

That aside, i assume you’re still in high school, probably first or second year, seeing the exercises you often ask us to help you solve, i have to tell you, if you find this stuff hard and you want to be an architect, you’ve got to seriously start chomping numbers.

Architecture is ALL numbers, Renzo Piano and Frank Lloyd Wright can crunch the numbers needed to design those absurd buildings in ways that prevent them from collapsing. So can every other competent architect for the buildings he designs.

I’m not saying you should give up, but i suggest you start rebuilding your knowledge of mathematics from the bottom up, or improve it, because this level won’t cut it. I never had any problems with that kind of stuff and I’m in all kinds of shit now that I’m in uni.

As for doing something because you need it for somewhere else, there is nothing wrong with that, what’s odd is that you don’t get satisfaction out of being one step closer to your goal.

The basic principle is that if a*b=0 then either a=0 or b=0 or both.
Before dividing out a common factor from an equation you should check for a solution where the factor itself equals zero.

@Thammuz I’m a non-traditional student in college. The reason I don’t know this stuff is cuz it’s been a decade since I learned it, so I had to re-take some classes, and my professor is no help. That doesn’t mean I can’t get it.

@papayalily That doesn’t mean I can’t get it.

I know, that’s why i didn’t say you should give up. But you need to practice a lot or find someone that can help you get even with the knowledges you lack/have lost touch with because, at least for my university’s standards, you wouldn’t even pass the enrollment test.

To give you an idea, my university’s most basic math course takes this stuff as learned and doesn’t even mention it.

Out of curiosity, are these subjects part of college education or are you taking them because of your “non traditional” status, which i’m not really sure what should entail?

@Thammuz I’m doing a year at a cheap state school for gen-ed before going to the school that has the architecture program. This particular class is a remedial class; as a general rule, non-trads will have to take at least one remedial class to jog their memory.
FWIW, the school that I’m going to next year only requires 1 math class for their architecture degree, and it can be “Math Visuals”.

@papayalily Good god i hope (for your sake as well as that of your clients’) you’re really good at it on your own, and i hope i never get in a building designed by someone who got his degree at that school without someone else proofreading his blueprints, considering a small mistake in stability calculations can be the difference between “all is well” and “OH MY GOD MY LEGS ARE STUCK UNDER A PILE OF DEBRIS”.

@Thammuz Ok, seriously, what is wrong with asking for help? Without a good teacher, almost all subjects are hard to learn. Where are you getting this idea that I’m somehow horrible at stuff instead of just refreshing my memory? Do you remember everything you learned in high school? I thought I could come here and ask for help, and instead, because I have a couple moments of confusing you think I’m gigantically incompetent? WTF?
You almost definitely have gotten into a building designed by someone from that school. It’s one of the top architecture programs in the country

@papayalily Ok, CHILL. First and foremost, yes, i do remember everything i studied in high school, i got out of there two years ago.

My suggestion of finding someone that can help you IRL (aka: a good teacher) is simply because i myself have seen your questions at least three times and all those i’ve seen pertain to first year high-school algebra here in Italy. All things that, as far as my knowledge goes, are pretty fucking necessary for physics calculations and therefore for architecture.

I don’t know what’s the extent of high school algebra in the US but we go as far as definite and indefinite integrals, which is light-years away from your current position. Which had me worried your backlog of things you should rehash went a little farther than you could study in a year with a professor that “is no help” and asking on the internet.

That said, there’s nothing wrong with asking, and, as you already saw, i try to help when i can, all i was suggesting is that you don’t rely only on us because, if the backlog is as big as i think, that’s not going to be enough.

As for the critique of the school, i stand by my judgment. An architecture program that doesn’t mandate advanced calculus and advanced analysis (or whatever your equivalent may be) is not an architecture program i would suggest, unless those were prerequisites, in which case I’d say it does “require” it. (Again, I’m not familiar with your education system, so i don’t know how that’s supposed to work, if you can enlighten me, I’d appreciate it)

@Thammuz But it’s not like I have to get my degree within 4 years or never…. It doesn’t matter where I am, it matters where I will end up by the time I’m done.

@papayalily I absolutely agree, i myself have a year worth of exams i still have to give, but i was under the impression you had to cover all that ground in one year, which led me to suggest stronger measures.

@Thammuz No, I have as long as I need. And remember, we do have licensures, so even if you don’t care for the program, I can’t practice unless I pass the state test.