48x^2-3v^4x^2=0

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Solution for 48x^2-3v^4x^2=0 equation:


Simplifying
48x2 + -3v4x2 = 0

Reorder the terms:
-3v4x2 + 48x2 = 0

Solving
-3v4x2 + 48x2 = 0

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '-48x2' to each side of the equation.
-3v4x2 + 48x2 + -48x2 = 0 + -48x2

Combine like terms: 48x2 + -48x2 = 0
-3v4x2 + 0 = 0 + -48x2
-3v4x2 = 0 + -48x2
Remove the zero:
-3v4x2 = -48x2

Divide each side by '-3x2'.
v4 = 16

Simplifying
v4 = 16

Reorder the terms:
-16 + v4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + v4 = 0

Factor a difference between two squares.
(4 + v2)(-4 + v2) = 0

Factor a difference between two squares.
(4 + v2)((2 + v)(-2 + v)) = 0

Subproblem 1

Set the factor '(4 + v2)' equal to zero and attempt to solve: Simplifying 4 + v2 = 0 Solving 4 + v2 = 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 + v2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v2 = 0 + -4 v2 = 0 + -4 Combine like terms: 0 + -4 = -4 v2 = -4 Simplifying v2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

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 = {-2, 2}

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