(x+12)(x+3)+(5x-6)=180

Solution for (x+12)(x+3)+(5x-6)=180 equation:

(x+12)(x+3)+(5x-6)=180

We move all terms to the left:

(x+12)(x+3)+(5x-6)-(180)=0

We get rid of parentheses

(x+12)(x+3)+5x-6-180=0

We multiply parentheses ..

(+x^2+3x+12x+36)+5x-6-180=0

We add all the numbers together, and all the variables

(+x^2+3x+12x+36)+5x-186=0

We get rid of parentheses

x^2+3x+12x+5x+36-186=0

We add all the numbers together, and all the variables

x^2+20x-150=0

a = 1; b = 20; c = -150;
Δ = b2-4ac
Δ = 202-4·1·(-150)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{10}}{2*1}=\frac{-20-10\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{10}}{2*1}=\frac{-20+10\sqrt{10}}{2}
$