-3k(6k+6)=-8-6k+4

Solution for -3k(6k+6)=-8-6k+4 equation:

-3k(6k+6)=-8-6k+4

We move all terms to the left:

-3k(6k+6)-(-8-6k+4)=0

We add all the numbers together, and all the variables

-3k(6k+6)-(-6k-4)=0

We multiply parentheses

-18k^2-18k-(-6k-4)=0

We get rid of parentheses

-18k^2-18k+6k+4=0

We add all the numbers together, and all the variables

-18k^2-12k+4=0

a = -18; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-18)·4
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*-18}=\frac{12-12\sqrt{3}}{-36}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*-18}=\frac{12+12\sqrt{3}}{-36}
$