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

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Solution for 0=-x^4+2x^2-1 equation: 


Simplifying
0 = -1x4 + 2x2 + -1

Reorder the terms:
0 = -1 + 2x2 + -1x4

Solving
0 = -1 + 2x2 + -1x4

Solving for variable 'x'.

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

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

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

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

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

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

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

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


Subproblem 1
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 2
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

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

Subproblem 4
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, -1, 1}

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