9x^4+31x^2-20=0

Solution for 9x^4+31x^2-20=0 equation:

Simplifying
9x4 + 31x2 + -20 = 0

Reorder the terms:
-20 + 31x2 + 9x4 = 0

Solving
-20 + 31x2 + 9x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x2)(5 + -9x2) = 0

Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

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 '(5 + -9x2)' equal to zero and attempt to solve:

Simplifying
5 + -9x2 = 0

Solving
5 + -9x2 = 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 + -9x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x2 = 0 + -5
-9x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9x2 = -5

Divide each side by '-9'.
x2 = 0.5555555556

Simplifying
x2 = 0.5555555556

Take the square root of each side:
x = {-0.745355993, 0.745355993}
Solution
x = {-0.745355993, 0.745355993}