6k^2-108=-3k

Solution for 6k^2-108=-3k equation:

Simplifying
6k2 + -108 = -3k

Reorder the terms:
-108 + 6k2 = -3k

Solving
-108 + 6k2 = -3k

Solving for variable 'k'.

Reorder the terms:
-108 + 3k + 6k2 = -3k + 3k

Combine like terms: -3k + 3k = 0
-108 + 3k + 6k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + k + 2k2) = 0

Factor a trinomial.
3((-9 + -2k)(4 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -2k)' equal to zero and attempt to solve:

Simplifying
-9 + -2k = 0

Solving
-9 + -2k = 0

Move all terms containing k to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -2k = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2k = 0 + 9
-2k = 0 + 9

Combine like terms: 0 + 9 = 9
-2k = 9

Divide each side by '-2'.
k = -4.5

Simplifying
k = -4.5
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-4.5, 4}