8u^3-2u=0

Solution for 8u^3-2u=0 equation:

Simplifying
8u3 + -2u = 0

Reorder the terms:
-2u + 8u3 = 0

Solving
-2u + 8u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(-1 + 4u2) = 0

Factor a difference between two squares.
2u((1 + 2u)(-1 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

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

Simplifying
1 + 2u = 0

Solving
1 + 2u = 0

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

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

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

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

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

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

Simplifying
-1 + 2u = 0

Solving
-1 + 2u = 0

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

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

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

Combine like terms: 0 + 1 = 1
2u = 1

Divide each side by '2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {0, -0.5, 0.5}