(2x+6)(-3x+12)=0

Solution for (2x+6)(-3x+12)=0 equation:

(2x+6)(-3x+12)=0

We multiply parentheses ..

(-6x^2+24x-18x+72)=0

We get rid of parentheses

-6x^2+24x-18x+72=0

We add all the numbers together, and all the variables

-6x^2+6x+72=0

a = -6; b = 6; c = +72;
Δ = b2-4ac
Δ = 62-4·(-6)·72
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*-6}=\frac{36}{-12}
=-3
$