4-4x^2=x^4-1

Solution for 4-4x^2=x^4-1 equation:

Simplifying
4 + -4x2 = x4 + -1

Reorder the terms:
4 + -4x2 = -1 + x4

Solving
4 + -4x2 = -1 + x4

Solving for variable 'x'.

Reorder the terms:
4 + 1 + -4x2 + -1x4 = -1 + x4 + 1 + -1x4

Combine like terms: 4 + 1 = 5
5 + -4x2 + -1x4 = -1 + x4 + 1 + -1x4

Reorder the terms:
5 + -4x2 + -1x4 = -1 + 1 + x4 + -1x4

Combine like terms: -1 + 1 = 0
5 + -4x2 + -1x4 = 0 + x4 + -1x4
5 + -4x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
5 + -4x2 + -1x4 = 0

Factor a trinomial.
(1 + -1x2)(5 + x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(5 + x2) = 0

Subproblem 1
Set the factor '(5 + x2)' equal to zero and attempt to solve:

Simplifying
5 + x2 = 0

Solving
5 + x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x2 = 0 + -5
x2 = 0 + -5

Combine like terms: 0 + -5 = -5
x2 = -5

Simplifying
x2 = -5

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

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