9k^3-k=0

Solution for 9k^3-k=0 equation:

Simplifying
9k3 + -1k = 0

Reorder the terms:
-1k + 9k3 = 0

Solving
-1k + 9k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-1 + 9k2) = 0

Factor a difference between two squares.
k((1 + 3k)(-1 + 3k)) = 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 + 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
Subproblem 3
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, -0.3333333333, 0.3333333333}