6v^3+9v^2=0

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

Simplifying
6v3 + 9v2 = 0

Reorder the terms:
9v2 + 6v3 = 0

Solving
9v2 + 6v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v2'.
3v2(3 + 2v) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

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

Simplifying
3 + 2v = 0

Solving
3 + 2v = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2v = 0 + -3

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

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

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

Simplifying
v = -1.5
Solution
v = {0, -1.5}