3r^3+9r^2=0

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

Simplifying
3r3 + 9r2 = 0

Reorder the terms:
9r2 + 3r3 = 0

Solving
9r2 + 3r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r2'.
3r2(3 + r) = 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 '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

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

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

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

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