(x+8)(x)+(x+4)(x+12)=(x+8)(x)+160

Solution for (x+8)(x)+(x+4)(x+12)=(x+8)(x)+160 equation:

(x+8)(x)+(x+4)(x+12)=(x+8)(x)+160

We move all terms to the left:

(x+8)(x)+(x+4)(x+12)-((x+8)(x)+160)=0

We multiply parentheses

x^2+8x+(x+4)(x+12)-((x+8)x+160)=0

We multiply parentheses ..

x^2+(+x^2+12x+4x+48)+8x-((x+8)x+160)=0


We calculate terms in parentheses: -((x+8)x+160), so:

(x+8)x+160

We multiply parentheses

x^2+8x+160

Back to the equation:

-(x^2+8x+160)


We get rid of parentheses

x^2+x^2-x^2+12x+4x+8x-8x+48-160=0

We add all the numbers together, and all the variables

x^2+16x-112=0

a = 1; b = 16; c = -112;
Δ = b2-4ac
Δ = 162-4·1·(-112)
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{11}}{2*1}=\frac{-16-8\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{11}}{2*1}=\frac{-16+8\sqrt{11}}{2}
$