8k^3-k=0

Solution for 8k^3-k=0 equation:

Simplifying
8k3 + -1k = 0

Reorder the terms:
-1k + 8k3 = 0

Solving
-1k + 8k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-1 + 8k2) = 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 + 8k2)' equal to zero and attempt to solve:

Simplifying
-1 + 8k2 = 0

Solving
-1 + 8k2 = 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 + 8k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8k2 = 0 + 1
8k2 = 0 + 1

Combine like terms: 0 + 1 = 1
8k2 = 1

Divide each side by '8'.
k2 = 0.125

Simplifying
k2 = 0.125

Take the square root of each side:
k = {-0.353553391, 0.353553391}
Solution
k = {0, -0.353553391, 0.353553391}