-6k^2-5k-1=0

Solution for -6k^2-5k-1=0 equation:

Simplifying
-6k2 + -5k + -1 = 0

Reorder the terms:
-1 + -5k + -6k2 = 0

Solving
-1 + -5k + -6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 5k + 6k2) = 0

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

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

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 2
Set the factor '(1 + 3k)' equal to zero and attempt to solve:

Simplifying
1 + 3k = 0

Solving
1 + 3k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3k = 0 + -1
3k = 0 + -1

Combine like terms: 0 + -1 = -1
3k = -1

Divide each side by '3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Solution
k = {-0.5, -0.3333333333}