Z^3+Z=0

Solution for Z^3+Z=0 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}