0=x^4-9x^2+20

Solution for 0=x^4-9x^2+20 equation:

Simplifying
0 = x4 + -9x2 + 20

Reorder the terms:
0 = 20 + -9x2 + x4

Solving
0 = 20 + -9x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -20 = -20
-20 + 9x2 + -1x4 = 20 + -9x2 + x4 + -20 + 9x2 + -1x4

Reorder the terms:
-20 + 9x2 + -1x4 = 20 + -20 + -9x2 + 9x2 + x4 + -1x4

Combine like terms: 20 + -20 = 0
-20 + 9x2 + -1x4 = 0 + -9x2 + 9x2 + x4 + -1x4
-20 + 9x2 + -1x4 = -9x2 + 9x2 + x4 + -1x4

Combine like terms: -9x2 + 9x2 = 0
-20 + 9x2 + -1x4 = 0 + x4 + -1x4
-20 + 9x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-20 + 9x2 + -1x4 = 0

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

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

Take the square root of each side:
x = {-2.236067978, 2.236067978}
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 = {-2.236067978, 2.236067978, -2, 2}