r^6-9r^4=0

Solution for r^6-9r^4=0 equation:

Simplifying
r6 + -9r4 = 0

Reorder the terms:
-9r4 + r6 = 0

Solving
-9r4 + r6 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r4'.
r4(-9 + r2) = 0

Factor a difference between two squares.
r4((3 + r)(-3 + r)) = 0

Subproblem 1
Set the factor 'r4' equal to zero and attempt to solve:

Simplifying
r4 = 0

Solving
r4 = 0

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

Simplifying
r4 = 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 '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Subproblem 3
Set the factor '(-3 + r)' equal to zero and attempt to solve:

Simplifying
-3 + r = 0

Solving
-3 + r = 0

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

Add '3' to each side of the equation.
-3 + 3 + r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + r = 0 + 3
r = 0 + 3

Combine like terms: 0 + 3 = 3
r = 3

Simplifying
r = 3
Solution
r = {-3, 3}