Can someone help me explain how factoring is used to solve quadratic equations? I can't find an explaination anywhere.

say for example

x^2-3x+2 = 0

factor that left side

(x-2)(x-1) = 0

That tells you that if x = 2, the function is zero, because (2-2)=0
It also tells you that if x = 1, the function is zero. (1-1) = 0
so the solution is x = 2 or x = 1