(3x+12)(2x-32)=180

Solution for (3x+12)(2x-32)=180 equation:

(3x+12)(2x-32)=180

We move all terms to the left:

(3x+12)(2x-32)-(180)=0

We multiply parentheses ..

(+6x^2-96x+24x-384)-180=0

We get rid of parentheses

6x^2-96x+24x-384-180=0

We add all the numbers together, and all the variables

6x^2-72x-564=0

a = 6; b = -72; c = -564;
Δ = b2-4ac
Δ = -722-4·6·(-564)
Δ = 18720
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:

$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{130}}{2*6}=\frac{72-12\sqrt{130}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{130}}{2*6}=\frac{72+12\sqrt{130}}{12}
$