(x+8)(-4-x)=-96

Solution for (x+8)(-4-x)=-96 equation:

(x+8)(-4-x)=-96

We move all terms to the left:

(x+8)(-4-x)-(-96)=0

We add all the numbers together, and all the variables

(x+8)(-1x-4)-(-96)=0

We add all the numbers together, and all the variables

(x+8)(-1x-4)+96=0

We multiply parentheses ..

(-1x^2-4x-8x-32)+96=0

We get rid of parentheses

-1x^2-4x-8x-32+96=0

We add all the numbers together, and all the variables

-1x^2-12x+64=0

a = -1; b = -12; c = +64;
Δ = b2-4ac
Δ = -122-4·(-1)·64
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*-1}=\frac{32}{-2}
=-16
$