9r^3+6r^2=0

Solution for 9r^3+6r^2=0 equation:

Simplifying
9r3 + 6r2 = 0

Reorder the terms:
6r2 + 9r3 = 0

Solving
6r2 + 9r3 = 0

Solving for variable 'r'.

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

Ignore the factor 3.
Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

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

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

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

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Solution
r = {0, -0.6666666667}