(X+6)(3x+2)+12=180

Solution for (X+6)(3x+2)+12=180 equation:

(X+6)(3X+2)+12=180

We move all terms to the left:

(X+6)(3X+2)+12-(180)=0

We add all the numbers together, and all the variables

(X+6)(3X+2)-168=0

We multiply parentheses ..

(+3X^2+2X+18X+12)-168=0

We get rid of parentheses

3X^2+2X+18X+12-168=0

We add all the numbers together, and all the variables

3X^2+20X-156=0

a = 3; b = 20; c = -156;
Δ = b2-4ac
Δ = 202-4·3·(-156)
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{142}}{2*3}=\frac{-20-4\sqrt{142}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{142}}{2*3}=\frac{-20+4\sqrt{142}}{6}
$