X2-12x+21=-6 solve the quadratic by factoring

(x-3)(x-9)

Step-by-step explanation:

first thing you need to do is move the -6 over. so we're going to add 6 to both sides (we add because it's negative 6 and we need 0 on the right side)

so you have: x^2-12x+27

now we need to come up with two numbers that add to -12 and multiply to 27.

the factors of 27 are 9 & 3 and 27 & 1. only 9 & 3 add to 12 so we are going to use those.

since the 12 is negative however, 9 and 3 should both be negative.

therefore we get: (x-3)(x-9)

*it doesn't matter which order you put them in!