r^5-r^2=0

Solution for r^5-r^2=0 equation:

Simplifying
r5 + -1r2 = 0

Reorder the terms:
-1r2 + r5 = 0

Solving
-1r2 + r5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-1 + r3) = 0

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
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}