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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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