17v^2=-3v^3-14v

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Solution for 17v^2=-3v^3-14v equation: 


Simplifying
17v2 = -3v3 + -14v

Reorder the terms:
17v2 = -14v + -3v3

Solving
17v2 = -14v + -3v3

Solving for variable 'v'.

Reorder the terms:
14v + 17v2 + 3v3 = -14v + -3v3 + 14v + 3v3

Reorder the terms:
14v + 17v2 + 3v3 = -14v + 14v + -3v3 + 3v3

Combine like terms: -14v + 14v = 0
14v + 17v2 + 3v3 = 0 + -3v3 + 3v3
14v + 17v2 + 3v3 = -3v3 + 3v3

Combine like terms: -3v3 + 3v3 = 0
14v + 17v2 + 3v3 = 0

Factor out the Greatest Common Factor (GCF), 'v'.
v(14 + 17v + 3v2) = 0

Factor a trinomial.
v((14 + 3v)(1 + v)) = 0


Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0

Subproblem 2
Set the factor '(14 + 3v)' equal to zero and attempt to solve:

Simplifying
14 + 3v = 0

Solving
14 + 3v = 0

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

Add '-14' to each side of the equation.
14 + -14 + 3v = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3v = 0 + -14
3v = 0 + -14

Combine like terms: 0 + -14 = -14
3v = -14

Divide each side by '3'.
v = -4.666666667

Simplifying
v = -4.666666667

Subproblem 3
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 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 + v = 0 + -1

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

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

Simplifying
v = -1
Solution
v = {0, -4.666666667, -1}

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