2v^4-8=0

Solution for 2v^4-8=0 equation:

Simplifying
2v4 + -8 = 0

Reorder the terms:
-8 + 2v4 = 0

Solving
-8 + 2v4 = 0

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + 2v4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2v4 = 0 + 8
2v4 = 0 + 8

Combine like terms: 0 + 8 = 8
2v4 = 8

Divide each side by '2'.
v4 = 4

Simplifying
v4 = 4

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

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

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

Subproblem 1
Set the factor '(2 + v2)' equal to zero and attempt to solve:

Simplifying
2 + v2 = 0

Solving
2 + v2 = 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 + v2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v2 = 0 + -2
v2 = 0 + -2

Combine like terms: 0 + -2 = -2
v2 = -2

Simplifying
v2 = -2

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 + v2)' equal to zero and attempt to solve:

Simplifying
-2 + v2 = 0

Solving
-2 + v2 = 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 + v2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + v2 = 0 + 2
v2 = 0 + 2

Combine like terms: 0 + 2 = 2
v2 = 2

Simplifying
v2 = 2

Take the square root of each side:
v = {-1.414213562, 1.414213562}
Solution
v = {-1.414213562, 1.414213562}