a^3+3a=0

Solution for a^3+3a=0 equation:

Simplifying
a3 + 3a = 0

Reorder the terms:
3a + a3 = 0

Solving
3a + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(3 + a2) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(3 + a2)' equal to zero and attempt to solve:

Simplifying
3 + a2 = 0

Solving
3 + a2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a2 = 0 + -3
a2 = 0 + -3

Combine like terms: 0 + -3 = -3
a2 = -3

Simplifying
a2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}