s^4+s^2=20

Solution for s^4+s^2=20 equation:

Simplifying
s4 + s2 = 20

Reorder the terms:
s2 + s4 = 20

Solving
s2 + s4 = 20

Solving for variable 's'.

Reorder the terms:
-20 + s2 + s4 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + s2 + s4 = 0

Factor a trinomial.
(-5 + -1s2)(4 + -1s2) = 0

Factor a difference between two squares.
(-5 + -1s2)((2 + s)(2 + -1s)) = 0

Subproblem 1
Set the factor '(-5 + -1s2)' equal to zero and attempt to solve:

Simplifying
-5 + -1s2 = 0

Solving
-5 + -1s2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1s2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1s2 = 0 + 5
-1s2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1s2 = 5

Divide each side by '-1'.
s2 = -5

Simplifying
s2 = -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 + s)' equal to zero and attempt to solve:

Simplifying
2 + s = 0

Solving
2 + s = 0

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

Add '-2' to each side of the equation.
2 + -2 + s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + s = 0 + -2
s = 0 + -2

Combine like terms: 0 + -2 = -2
s = -2

Simplifying
s = -2
Subproblem 3
Set the factor '(2 + -1s)' equal to zero and attempt to solve:

Simplifying
2 + -1s = 0

Solving
2 + -1s = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1s = 0 + -2
-1s = 0 + -2

Combine like terms: 0 + -2 = -2
-1s = -2

Divide each side by '-1'.
s = 2

Simplifying
s = 2
Solution
s = {-2, 2}