Simplifying
x^{4} + -1x^{2} = 0
Reorder the terms:
-1x^{2} + x^{4} = 0
Solving
-1x^{2} + x^{4} = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x^{2}'.
x^{2}(-1 + x^{2}) = 0
Factor a difference between two squares.
x^{2}((1 + x)(-1 + x)) = 0
#### Subproblem 1

Set the factor 'x^{2}' equal to zero and attempt to solve:
Simplifying
x^{2} = 0
Solving
x^{2} = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x^{2} = 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}