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

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

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

We multiply parentheses ..

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

We multiply parentheses

12x^2-4x-6x+2=0

We add all the numbers together, and all the variables

12x^2-10x+2=0

a = 12; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·12·2
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*12}=\frac{8}{24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*12}=\frac{12}{24}
=1/2
$