3(x-3)(4x-4)=0

Solution for 3(x-3)(4x-4)=0 equation:

3(x-3)(4x-4)=0

We multiply parentheses ..

3(+4x^2-4x-12x+12)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

12x^2-48x+36=0

a = 12; b = -48; c = +36;
Δ = b2-4ac
Δ = -482-4·12·36
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24}{2*12}=\frac{24}{24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24}{2*12}=\frac{72}{24}
=3
$