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

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

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

We move all terms to the left:

0-((2x+6)(3x+12))=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 calculate terms in parentheses: -((+6x^2+24x+18x+72)), so:

(+6x^2+24x+18x+72)

We get rid of parentheses

6x^2+24x+18x+72

We add all the numbers together, and all the variables

6x^2+42x+72

Back to the equation:

-(6x^2+42x+72)


We get rid of parentheses

-6x^2-42x-72=0

a = -6; b = -42; c = -72;
Δ = b2-4ac
Δ = -422-4·(-6)·(-72)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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