42=(x-6)(x-6)*3

Solution for 42=(x-6)(x-6)*3 equation:

42=(x-6)(x-6)*3

We move all terms to the left:

42-((x-6)(x-6)*3)=0

We multiply parentheses ..

-((+x^2-6x-6x+36)*3)+42=0


We calculate terms in parentheses: -((+x^2-6x-6x+36)*3), so:

(+x^2-6x-6x+36)*3

We multiply parentheses

3x^2-18x-18x+108

We add all the numbers together, and all the variables

3x^2-36x+108

Back to the equation:

-(3x^2-36x+108)


We get rid of parentheses

-3x^2+36x-108+42=0

We add all the numbers together, and all the variables

-3x^2+36x-66=0

a = -3; b = 36; c = -66;
Δ = b2-4ac
Δ = 362-4·(-3)·(-66)
Δ = 504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{14}}{2*-3}=\frac{-36-6\sqrt{14}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{14}}{2*-3}=\frac{-36+6\sqrt{14}}{-6}
$