0=3(x-6)(x-2)

Solution for 0=3(x-6)(x-2) equation:

0=3(x-6)(x-2)

We move all terms to the left:

0-(3(x-6)(x-2))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-(3(+x^2-2x-6x+12))=0


We calculate terms in parentheses: -(3(+x^2-2x-6x+12)), so:

3(+x^2-2x-6x+12)

We multiply parentheses

3x^2-6x-18x+36

We add all the numbers together, and all the variables

3x^2-24x+36

Back to the equation:

-(3x^2-24x+36)


We get rid of parentheses

-3x^2+24x-36=0

a = -3; b = 24; c = -36;
Δ = b2-4ac
Δ = 242-4·(-3)·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-3}=\frac{-12}{-6}
=+2
$