12v^3-48v=0

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Solution for 12v^3-48v=0 equation:


Simplifying
12v3 + -48v = 0

Reorder the terms:
-48v + 12v3 = 0

Solving
-48v + 12v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '12v'.
12v(-4 + v2) = 0

Factor a difference between two squares.
12v((2 + v)(-2 + v)) = 0

Ignore the factor 12.

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 '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2

Subproblem 3

Set the factor '(-2 + v)' equal to zero and attempt to solve: Simplifying -2 + v = 0 Solving -2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + v = 0 + 2 v = 0 + 2 Combine like terms: 0 + 2 = 2 v = 2 Simplifying v = 2

Solution

v = {0, -2, 2}

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