4v^3-16v^2=180v

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Solution for 4v^3-16v^2=180v equation:


Simplifying
4v3 + -16v2 = 180v

Reorder the terms:
-16v2 + 4v3 = 180v

Solving
-16v2 + 4v3 = 180v

Solving for variable 'v'.

Reorder the terms:
-180v + -16v2 + 4v3 = 180v + -180v

Combine like terms: 180v + -180v = 0
-180v + -16v2 + 4v3 = 0

Factor out the Greatest Common Factor (GCF), '4v'.
4v(-45 + -4v + v2) = 0

Factor a trinomial.
4v((-5 + -1v)(9 + -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 '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5

Subproblem 3

Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9

Solution

v = {0, -5, 9}

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