2r^3+3r^2=9r

Solution for 2r^3+3r^2=9r equation:

Simplifying
2r3 + 3r2 = 9r

Reorder the terms:
3r2 + 2r3 = 9r

Solving
3r2 + 2r3 = 9r

Solving for variable 'r'.

Reorder the terms:
-9r + 3r2 + 2r3 = 9r + -9r

Combine like terms: 9r + -9r = 0
-9r + 3r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-9 + 3r + 2r2) = 0

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

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 '(-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 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {0, -3, 1.5}