How to convince my mom to let me move out?

I’m 15 and at my house there is some problems I’m not going to say specific details but its starting to push me to my limits. I just need to leave at least for a little while until things get better. My friends parents said I could move in with her and I know plenty of people who wouldn’t mind me staying at there house for a while its just my mom and I have has a conversation already about it but she just want listen. I love her to death but I need to leave until things get better. I just don’t know how to convince her.