3r^5+18r^3-3r^3-18r=0

Solution for 3r^5+18r^3-3r^3-18r=0 equation:

Simplifying
3r5 + 18r3 + -3r3 + -18r = 0

Reorder the terms:
-18r + 18r3 + -3r3 + 3r5 = 0

Combine like terms: 18r3 + -3r3 = 15r3
-18r + 15r3 + 3r5 = 0

Solving
-18r + 15r3 + 3r5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-6 + 5r2 + r4) = 0

Factor a trinomial.
3r((-6 + -1r2)(1 + -1r2)) = 0

Factor a difference between two squares.
3r((-6 + -1r2)((1 + r)(1 + -1r))) = 0

Ignore the factor 3.
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 '(-6 + -1r2)' equal to zero and attempt to solve:

Simplifying
-6 + -1r2 = 0

Solving
-6 + -1r2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r2 = 0 + 6
-1r2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1r2 = 6

Divide each side by '-1'.
r2 = -6

Simplifying
r2 = -6

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 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 1

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