9*r^3+36*r^2=108*r

Solution for 9*r^3+36*r^2=108*r equation:

Simplifying
9r3 + 36r2 = 108r

Reorder the terms:
36r2 + 9r3 = 108r

Solving
36r2 + 9r3 = 108r

Solving for variable 'r'.

Reorder the terms:
-108r + 36r2 + 9r3 = 108r + -108r

Combine like terms: 108r + -108r = 0
-108r + 36r2 + 9r3 = 0

Factor out the Greatest Common Factor (GCF), '9r'.
9r(-12 + 4r + r2) = 0

Factor a trinomial.
9r((-6 + -1r)(2 + -1r)) = 0

Ignore the factor 9.
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 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 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 + -1r = 0 + 6

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

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

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

Simplifying
r = -6
Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0, -6, 2}