10v^5+45v^4+45v^3=0

Solution for 10v^5+45v^4+45v^3=0 equation:

Simplifying
10v5 + 45v4 + 45v3 = 0

Reorder the terms:
45v3 + 45v4 + 10v5 = 0

Solving
45v3 + 45v4 + 10v5 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5v3'.
5v3(9 + 9v + 2v2) = 0

Factor a trinomial.
5v3((3 + v)(3 + 2v)) = 0

Ignore the factor 5.
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 '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

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

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

Simplifying
v = -3
Subproblem 3
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 = {-3, -1.5}