x^4-31x^2-180=0

Solution for x^4-31x^2-180=0 equation:

Simplifying
x4 + -31x2 + -180 = 0

Reorder the terms:
-180 + -31x2 + x4 = 0

Solving
-180 + -31x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x2)(36 + -1x2) = 0

Factor a difference between two squares.
(-5 + -1x2)((6 + x)(6 + -1x)) = 0

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

Simplifying
-5 + -1x2 = 0

Solving
-5 + -1x2 = 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 + -1x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x2 = 0 + 5
-1x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1x2 = 5

Divide each side by '-1'.
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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-6, 6}