4x^2 +28x -32 =0 solve this problem?

We know that if xy=0 then x or/and y=0

4x^2+28x-32=0
factor out the 4
4(x^2+7-8)=0

factor out the x^2+7-8
we must find out what two numbers multiply to get -8 and add to get 7
the numbers are 8 and -1

so 4[(x-1)(x+8)]=0

we know that if exg 4y=0 then y=0
so
therefor
(x-1)(x+8)=0
set each to zero
x-1=0
x=1
x+8=0
x=-8

x could be 1 or -8

Where are the following equations?