v^4-1=

Solution for v^4-1= equation:

Simplifying
v4 + -1 = 0

Reorder the terms:
-1 + v4 = 0

Solving
-1 + v4 = 0

Solving for variable 'v'.

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

Add '1' to each side of the equation.
-1 + 1 + v4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + v4 = 0 + 1
v4 = 0 + 1

Combine like terms: 0 + 1 = 1
v4 = 1

Simplifying
v4 = 1

Reorder the terms:
-1 + v4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + v4 = 0

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

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

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

Simplifying
1 + v2 = 0

Solving
1 + v2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + v2 = 0 + -1
v2 = 0 + -1

Combine like terms: 0 + -1 = -1
v2 = -1

Simplifying
v2 = -1

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 '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

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

Add '-1' to each side of the equation.
1 + -1 + v = 0 + -1

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

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

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

Simplifying
-1 + v = 0

Solving
-1 + v = 0

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

Add '1' to each side of the equation.
-1 + 1 + v = 0 + 1

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

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

Simplifying
v = 1
Solution
v = {-1, 1}