u^3-3u=0

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

Simplifying
u3 + -3u = 0

Reorder the terms:
-3u + u3 = 0

Solving
-3u + u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(-3 + u2) = 0

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 '(-3 + u2)' equal to zero and attempt to solve:

Simplifying
-3 + u2 = 0

Solving
-3 + u2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + u2 = 0 + 3
u2 = 0 + 3

Combine like terms: 0 + 3 = 3
u2 = 3

Simplifying
u2 = 3

Take the square root of each side:
u = {-1.732050808, 1.732050808}
Solution
u = {0, -1.732050808, 1.732050808}