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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

54x^2+36x-18=0

a = 54; b = 36; c = -18;
Δ = b2-4ac
Δ = 362-4·54·(-18)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-72}{2*54}=\frac{-108}{108}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+72}{2*54}=\frac{36}{108}
=1/3
$