v^2-4vx-12x^2=0

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Solution for v^2-4vx-12x^2=0 equation:


Simplifying
v2 + -4vx + -12x2 = 0

Reorder the terms:
-4vx + v2 + -12x2 = 0

Solving
-4vx + v2 + -12x2 = 0

Solving for variable 'v'.

Factor a trinomial.
(v + -6x)(v + 2x) = 0

Subproblem 1

Set the factor '(v + -6x)' equal to zero and attempt to solve: Simplifying v + -6x = 0 Solving v + -6x = 0 Move all terms containing v to the left, all other terms to the right. Add '6x' to each side of the equation. v + -6x + 6x = 0 + 6x Combine like terms: -6x + 6x = 0 v + 0 = 0 + 6x v = 0 + 6x Remove the zero: v = 6x Simplifying v = 6x

Subproblem 2

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

Solution

v = {6x, -2x}

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