5r^6-45r^2=

Solution for 5r^6-45r^2= equation:

Simplifying
5r6 + -45r2 = 0

Reorder the terms:
-45r2 + 5r6 = 0

Solving
-45r2 + 5r6 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r2'.
5r2(-9 + r4) = 0

Factor a difference between two squares.
5r2((3 + r2)(-3 + r2)) = 0

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

Simplifying
3 + r2 = 0

Solving
3 + r2 = 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 + r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r2 = 0 + -3
r2 = 0 + -3

Combine like terms: 0 + -3 = -3
r2 = -3

Simplifying
r2 = -3

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 '(-3 + r2)' equal to zero and attempt to solve:

Simplifying
-3 + r2 = 0

Solving
-3 + r2 = 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 + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + r2 = 0 + 3
r2 = 0 + 3

Combine like terms: 0 + 3 = 3
r2 = 3

Simplifying
r2 = 3

Take the square root of each side:
r = {-1.732050808, 1.732050808}
Solution
r = {0, -1.732050808, 1.732050808}