2(3x+12)(6x+9)=0

Solution for 2(3x+12)(6x+9)=0 equation:

2(3x+12)(6x+9)=0

We multiply parentheses ..

2(+18x^2+27x+72x+108)=0

We multiply parentheses

36x^2+54x+144x+216=0

We add all the numbers together, and all the variables

36x^2+198x+216=0

a = 36; b = 198; c = +216;
Δ = b2-4ac
Δ = 1982-4·36·216
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-90}{2*36}=\frac{-288}{72}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+90}{2*36}=\frac{-108}{72}
=-1+1/2
$