x^4-x^2=2x^2+4

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

Simplifying
x4 + -1x2 = 2x2 + 4

Reorder the terms:
-1x2 + x4 = 2x2 + 4

Reorder the terms:
-1x2 + x4 = 4 + 2x2

Solving
-1x2 + x4 = 4 + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -1x2 + -2x2 + x4 = 4 + 2x2 + -4 + -2x2

Combine like terms: -1x2 + -2x2 = -3x2
-4 + -3x2 + x4 = 4 + 2x2 + -4 + -2x2

Reorder the terms:
-4 + -3x2 + x4 = 4 + -4 + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + -3x2 + x4 = 0 + 2x2 + -2x2
-4 + -3x2 + x4 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -3x2 + x4 = 0

Factor a trinomial.
(-1 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-1 + -1x2)((2 + x)(2 + -1x)) = 0

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

Simplifying
-1 + -1x2 = 0

Solving
-1 + -1x2 = 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 + -1x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x2 = 0 + 1
-1x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1x2 = 1

Divide each side by '-1'.
x2 = -1

Simplifying
x2 = -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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}