(x+9)(x-3)=-32

Solution for (x+9)(x-3)=-32 equation:

(x+9)(x-3)=-32

We move all terms to the left:

(x+9)(x-3)-(-32)=0

We add all the numbers together, and all the variables

(x+9)(x-3)+32=0

We multiply parentheses ..

(+x^2-3x+9x-27)+32=0

We get rid of parentheses

x^2-3x+9x-27+32=0

We add all the numbers together, and all the variables

x^2+6x+5=0

a = 1; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*1}=\frac{-2}{2}
=-1
$