5k^2+12k-108=0

Solution for 5k^2+12k-108=0 equation:

Simplifying
5k2 + 12k + -108 = 0

Reorder the terms:
-108 + 12k + 5k2 = 0

Solving
-108 + 12k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-6 + -1k)(18 + -5k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(18 + -5k)' equal to zero and attempt to solve:

Simplifying
18 + -5k = 0

Solving
18 + -5k = 0

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

Add '-18' to each side of the equation.
18 + -18 + -5k = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -5k = 0 + -18
-5k = 0 + -18

Combine like terms: 0 + -18 = -18
-5k = -18

Divide each side by '-5'.
k = 3.6

Simplifying
k = 3.6
Solution
k = {-6, 3.6}