4v^3-16v^2-84v=0

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Solution for 4v^3-16v^2-84v=0 equation:


Simplifying
4v3 + -16v2 + -84v = 0

Reorder the terms:
-84v + -16v2 + 4v3 = 0

Solving
-84v + -16v2 + 4v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4v'.
4v(-21 + -4v + v2) = 0

Factor a trinomial.
4v((-3 + -1v)(7 + -1v)) = 0

Ignore the factor 4.

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 '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 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 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3

Subproblem 3

Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 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 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7

Solution

v = {0, -3, 7}

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