Have you heard of the AC factoring method and is this a good explanation?

I just learned about this way of simplifying the factorization of a quadratic equation. I don’t care much for the explanations I have seen for why it works. This is my take on it. I will show the proof by using a specific example.

Suppose we are given: 6x^^2 – x -2 = 0. Call this equation 1.
Multiply both sides by the leading coefficient, 6.
6(6x^^2 – x -2 = 0)=0
(6x)^^2 – (6x) – 12 = 0. Call this equation 2.
Let y = 6x
y^^2 – y – 12 =0. – This will always have the form y^^2 +by +ac=0
The expression is relatively easy to factor.
(y-4)(y+3)=0
Substituting back for y = 6x, we get
(6x – 4)(6x + 3) = 0.
This will give us the roots of the equation, but if we multiply it out, we are going to get equation 2, where everything is off by a factor of 6. We can factor the expression in equation 1 by getting rid of this factor of 6 by dividing (6x-4) by 2 and (6x + 3) by 3 giving:

6x^^2 – x -2 = (3x – 2)(2x + 1)