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

Solution for (x+6)(3x-12)=0 equation:

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

We multiply parentheses ..

(+3x^2-12x+18x-72)=0

We get rid of parentheses

3x^2-12x+18x-72=0

We add all the numbers together, and all the variables

3x^2+6x-72=0

a = 3; b = 6; c = -72;
Δ = b2-4ac
Δ = 62-4·3·(-72)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*3}=\frac{24}{6}
=4
$