-3x(x-4)=-3x+12

Solution for -3x(x-4)=-3x+12 equation:

-3x(x-4)=-3x+12

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+15x-12=0

a = -3; b = 15; c = -12;
Δ = b2-4ac
Δ = 152-4·(-3)·(-12)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-3}=\frac{-6}{-6}
=1
$