r^4+r=0

Solution for r^4+r=0 equation:

Simplifying
r4 + r = 0

Reorder the terms:
r + r4 = 0

Solving
r + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(1 + r3) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + r3)' equal to zero and attempt to solve:

Simplifying
1 + r3 = 0

Solving
1 + r3 = 0

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

Add '-1' to each side of the equation.
1 + -1 + r3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r3 = 0 + -1
r3 = 0 + -1

Combine like terms: 0 + -1 = -1
r3 = -1

Simplifying
r3 = -1

The solution to this equation could not be determined.

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