z^3+z=

Solution for z^3+z= equation:

Simplifying
z3 + z = 0

Reorder the terms:
z + z3 = 0

Solving
z + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(1 + z2) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(1 + z2)' equal to zero and attempt to solve:

Simplifying
1 + z2 = 0

Solving
1 + z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z2 = 0 + -1
z2 = 0 + -1

Combine like terms: 0 + -1 = -1
z2 = -1

Simplifying
z2 = -1

The solution to this equation could not be determined.

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