5r^5-5r=0

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

Simplifying
5r5 + -5r = 0

Reorder the terms:
-5r + 5r5 = 0

Solving
-5r + 5r5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-1 + r4) = 0

Factor a difference between two squares.
5r((1 + r2)(-1 + r2)) = 0

Factor a difference between two squares.
5r((1 + r2)((1 + r)(-1 + r))) = 0

Ignore the factor 5.
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 + r2)' equal to zero and attempt to solve:

Simplifying
1 + r2 = 0

Solving
1 + r2 = 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 + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r2 = 0 + -1
r2 = 0 + -1

Combine like terms: 0 + -1 = -1
r2 = -1

Simplifying
r2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

Simplifying
r = -1
Subproblem 4
Set the factor '(-1 + r)' equal to zero and attempt to solve:

Simplifying
-1 + r = 0

Solving
-1 + r = 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 + r = 0 + 1

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

Combine like terms: 0 + 1 = 1
r = 1

Simplifying
r = 1
Solution
r = {0, -1, 1}