-6k^2-13k-6=0

Solution for -6k^2-13k-6=0 equation:

Simplifying
-6k2 + -13k + -6 = 0

Reorder the terms:
-6 + -13k + -6k2 = 0

Solving
-6 + -13k + -6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 13k + 6k2) = 0

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

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

Simplifying
3 + 2k = 0

Solving
3 + 2k = 0

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

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

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

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

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
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 = {-1.5, -0.6666666667}