13k^3+12k^2-k=0

Solution for 13k^3+12k^2-k=0 equation:

Simplifying
13k3 + 12k2 + -1k = 0

Reorder the terms:
-1k + 12k2 + 13k3 = 0

Solving
-1k + 12k2 + 13k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-1 + 12k + 13k2) = 0

Factor a trinomial.
k((-1 + -1k)(1 + -13k)) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(-1 + -1k)' equal to zero and attempt to solve:

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 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 + -1k = 0 + 1

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

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

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

Simplifying
k = -1
Subproblem 3
Set the factor '(1 + -13k)' equal to zero and attempt to solve:

Simplifying
1 + -13k = 0

Solving
1 + -13k = 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 + -13k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -13k = 0 + -1
-13k = 0 + -1

Combine like terms: 0 + -1 = -1
-13k = -1

Divide each side by '-13'.
k = 0.07692307692

Simplifying
k = 0.07692307692
Solution
k = {0, -1, 0.07692307692}