r^7=r^5

Solution for r^7=r^5 equation:

Simplifying
r7 = r5

Solving
r7 = r5

Solving for variable 'r'.

Reorder the terms:
-1r5 + r7 = r5 + -1r5

Combine like terms: r5 + -1r5 = 0
-1r5 + r7 = 0

Factor out the Greatest Common Factor (GCF), 'r5'.
r5(-1 + r2) = 0

Factor a difference between two squares.
r5((1 + r)(-1 + r)) = 0

Subproblem 1
Set the factor 'r5' equal to zero and attempt to solve:

Simplifying
r5 = 0

Solving
r5 = 0

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

Simplifying
r5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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 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
Solution
r = {-1, 1}