2r^6-12r^5=-18r^4

Solution for 2r^6-12r^5=-18r^4 equation:

Simplifying
2r6 + -12r5 = -18r4

Reorder the terms:
-12r5 + 2r6 = -18r4

Solving
-12r5 + 2r6 = -18r4

Solving for variable 'r'.

Reorder the terms:
18r4 + -12r5 + 2r6 = -18r4 + 18r4

Combine like terms: -18r4 + 18r4 = 0
18r4 + -12r5 + 2r6 = 0

Factor out the Greatest Common Factor (GCF), '2r4'.
2r4(9 + -6r + r2) = 0

Factor a trinomial.
2r4((3 + -1r)(3 + -1r)) = 0

Ignore the factor 2.
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 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

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