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

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

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

We multiply parentheses ..

(+108x^2-54x+36x-18)=0

We get rid of parentheses

108x^2-54x+36x-18=0

We add all the numbers together, and all the variables

108x^2-18x-18=0

a = 108; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·108·(-18)
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{-(-18)-90}{2*108}=\frac{-72}{216}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+90}{2*108}=\frac{108}{216}
=1/2
$