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

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

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

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

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

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

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

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

Solving
-2x2 + x4 = -1x2

Solving for variable 'x'.

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

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

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

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

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

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 '(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 + 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
Solution
x = {0, -1, 1}