3v^3(2v^2+13v+6)=0

Solution for 3v^3(2v^2+13v+6)=0 equation:

Simplifying
3v3(2v2 + 13v + 6) = 0

Reorder the terms:
3v3(6 + 13v + 2v2) = 0
(6 * 3v3 + 13v * 3v3 + 2v2 * 3v3) = 0
(18v3 + 39v4 + 6v5) = 0

Solving
18v3 + 39v4 + 6v5 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v3'.
3v3(6 + 13v + 2v2) = 0

Factor a trinomial.
3v3((6 + v)(1 + 2v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'v3' equal to zero and attempt to solve:

Simplifying
v3 = 0

Solving
v3 = 0

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

Simplifying
v3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 3
Set the factor '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {-6, -0.5}