(12x-1)(-6x+3)=0

Solution for (12x-1)(-6x+3)=0 equation:

(12x-1)(-6x+3)=0

We multiply parentheses ..

(-72x^2+36x+6x-3)=0

We get rid of parentheses

-72x^2+36x+6x-3=0

We add all the numbers together, and all the variables

-72x^2+42x-3=0

a = -72; b = 42; c = -3;
Δ = b2-4ac
Δ = 422-4·(-72)·(-3)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*-72}=\frac{-72}{-144}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*-72}=\frac{-12}{-144}
=1/12
$