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

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

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

We multiply parentheses ..

(-12x^2+4x+36x-12)=0

We get rid of parentheses

-12x^2+4x+36x-12=0

We add all the numbers together, and all the variables

-12x^2+40x-12=0

a = -12; b = 40; c = -12;
Δ = b2-4ac
Δ = 402-4·(-12)·(-12)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-32}{2*-12}=\frac{-72}{-24}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+32}{2*-12}=\frac{-8}{-24}
=1/3
$