5r^3+9r^2=2r

Solution for 5r^3+9r^2=2r equation:

Simplifying
5r3 + 9r2 = 2r

Reorder the terms:
9r2 + 5r3 = 2r

Solving
9r2 + 5r3 = 2r

Solving for variable 'r'.

Reorder the terms:
-2r + 9r2 + 5r3 = 2r + -2r

Combine like terms: 2r + -2r = 0
-2r + 9r2 + 5r3 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-2 + 9r + 5r2) = 0

Factor a trinomial.
r((-2 + -1r)(1 + -5r)) = 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 '(-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
Subproblem 3
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

Solving
1 + -5r = 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 + -5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5r = 0 + -1
-5r = 0 + -1

Combine like terms: 0 + -1 = -1
-5r = -1

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {0, -2, 0.2}