12(x+3)=x(x+12)-108

Solution for 12(x+3)=x(x+12)-108 equation:

12(x+3)=x(x+12)-108

We move all terms to the left:

12(x+3)-(x(x+12)-108)=0

We multiply parentheses

12x-(x(x+12)-108)+36=0


We calculate terms in parentheses: -(x(x+12)-108), so:

x(x+12)-108

We multiply parentheses

x^2+12x-108

Back to the equation:

-(x^2+12x-108)


We get rid of parentheses

-x^2+12x-12x+108+36=0

We add all the numbers together, and all the variables

-1x^2+144=0

a = -1; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-1)·144
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-1}=\frac{24}{-2}
=-12
$