0=4v^4-64v^2

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Solution for 0=4v^4-64v^2 equation: 


Simplifying
0 = 4v4 + -64v2

Reorder the terms:
0 = -64v2 + 4v4

Solving
0 = -64v2 + 4v4

Solving for variable 'v'.
Remove the zero:
64v2 + -4v4 = -64v2 + 4v4 + 64v2 + -4v4

Reorder the terms:
64v2 + -4v4 = -64v2 + 64v2 + 4v4 + -4v4

Combine like terms: -64v2 + 64v2 = 0
64v2 + -4v4 = 0 + 4v4 + -4v4
64v2 + -4v4 = 4v4 + -4v4

Combine like terms: 4v4 + -4v4 = 0
64v2 + -4v4 = 0

Factor out the Greatest Common Factor (GCF), '4v2'.
4v2(16 + -1v2) = 0

Factor a difference between two squares.
4v2((4 + v)(4 + -1v)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}

Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 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 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4

Subproblem 3
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 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 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {0, -4, 4}

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