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

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

Simplifying
1 + -1x2 = x4 + 2x2 + 1

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

Add '-1' to each side of the equation.
1 + -1 + -1x2 = 1 + 2x2 + -1 + x4

Combine like terms: 1 + -1 = 0
0 + -1x2 = 1 + 2x2 + -1 + x4
-1x2 = 1 + 2x2 + -1 + x4

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

Combine like terms: 1 + -1 = 0
-1x2 = 0 + 2x2 + x4
-1x2 = 2x2 + x4

Solving
-1x2 = 2x2 + x4

Solving for variable 'x'.

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

Reorder the terms:
-3x2 + -1x4 = 2x2 + -2x2 + x4 + -1x4

Combine like terms: 2x2 + -2x2 = 0
-3x2 + -1x4 = 0 + x4 + -1x4
-3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-3x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(3 + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x2 = 0 + -3
x2 = 0 + -3

Combine like terms: 0 + -3 = -3
x2 = -3

Simplifying
x2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}