0=x^4+x^2-20

Solution for 0=x^4+x^2-20 equation:

Simplifying
0 = x4 + x2 + -20

Reorder the terms:
0 = -20 + x2 + x4

Solving
0 = -20 + x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -1x2 + -1x4 = -20 + x2 + x4 + 20 + -1x2 + -1x4

Reorder the terms:
20 + -1x2 + -1x4 = -20 + 20 + x2 + -1x2 + x4 + -1x4

Combine like terms: -20 + 20 = 0
20 + -1x2 + -1x4 = 0 + x2 + -1x2 + x4 + -1x4
20 + -1x2 + -1x4 = x2 + -1x2 + x4 + -1x4

Combine like terms: x2 + -1x2 = 0
20 + -1x2 + -1x4 = 0 + x4 + -1x4
20 + -1x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
20 + -1x2 + -1x4 = 0

Factor a trinomial.
(4 + -1x2)(5 + x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(5 + x2) = 0

Subproblem 1
Set the factor '(5 + x2)' equal to zero and attempt to solve:

Simplifying
5 + x2 = 0

Solving
5 + x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x2 = 0 + -5
x2 = 0 + -5

Combine like terms: 0 + -5 = -5
x2 = -5

Simplifying
x2 = -5

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}