36k^2+138k-108=0

Solution for 36k^2+138k-108=0 equation:

Simplifying
36k2 + 138k + -108 = 0

Reorder the terms:
-108 + 138k + 36k2 = 0

Solving
-108 + 138k + 36k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + 23k + 6k2) = 0

Factor a trinomial.
6((-9 + -2k)(2 + -3k)) = 0

Ignore the factor 6.
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 '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-4.5, 0.6666666667}