3v^3+33v^2+84v=0

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Solution for 3v^3+33v^2+84v=0 equation:


Simplifying
3v3 + 33v2 + 84v = 0

Reorder the terms:
84v + 33v2 + 3v3 = 0

Solving
84v + 33v2 + 3v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(28 + 11v + v2) = 0

Factor a trinomial.
3v((7 + v)(4 + v)) = 0

Ignore the factor 3.

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 '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7

Subproblem 3

Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4

Solution

v = {0, -7, -4}

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