96=(2x+8)(2x+12)+96

Solution for 96=(2x+8)(2x+12)+96 equation:

96=(2x+8)(2x+12)+96

We move all terms to the left:

96-((2x+8)(2x+12)+96)=0

We multiply parentheses ..

-((+4x^2+24x+16x+96)+96)+96=0


We calculate terms in parentheses: -((+4x^2+24x+16x+96)+96), so:

(+4x^2+24x+16x+96)+96

We get rid of parentheses

4x^2+24x+16x+96+96

We add all the numbers together, and all the variables

4x^2+40x+192

Back to the equation:

-(4x^2+40x+192)


We get rid of parentheses

-4x^2-40x-192+96=0

We add all the numbers together, and all the variables

-4x^2-40x-96=0

a = -4; b = -40; c = -96;
Δ = b2-4ac
Δ = -402-4·(-4)·(-96)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8}{2*-4}=\frac{32}{-8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8}{2*-4}=\frac{48}{-8}
=-6
$