4u^3-8u=0

Solution for 4u^3-8u=0 equation:

Simplifying
4u3 + -8u = 0

Reorder the terms:
-8u + 4u3 = 0

Solving
-8u + 4u3 = 0

Solving for variable 'u'.

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

Ignore the factor 4.
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 '(-2 + u2)' equal to zero and attempt to solve:

Simplifying
-2 + u2 = 0

Solving
-2 + u2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + u2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + u2 = 0 + 2
u2 = 0 + 2

Combine like terms: 0 + 2 = 2
u2 = 2

Simplifying
u2 = 2

Take the square root of each side:
u = {-1.414213562, 1.414213562}
Solution
u = {0, -1.414213562, 1.414213562}