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

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

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

We multiply parentheses ..

(-54x^2-18x+18x+6)=0

We get rid of parentheses

-54x^2-18x+18x+6=0

We add all the numbers together, and all the variables

-54x^2+6=0

a = -54; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-54)·6
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-54}=\frac{-36}{-108}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-54}=\frac{36}{-108}
=-1/3
$