(6x-3)(2x+1)=0

Solution for (6x-3)(2x+1)=0 equation:

(6x-3)(2x+1)=0

We multiply parentheses ..

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

We get rid of parentheses

12x^2+6x-6x-3=0

We add all the numbers together, and all the variables

12x^2-3=0

a = 12; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·12·(-3)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*12}=\frac{12}{24}
=1/2
$