x^4+8x^2-240=0

Solution for x^4+8x^2-240=0 equation:

Simplifying
x4 + 8x2 + -240 = 0

Reorder the terms:
-240 + 8x2 + x4 = 0

Solving
-240 + 8x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-20 + -1x2)(12 + -1x2) = 0

Subproblem 1
Set the factor '(-20 + -1x2)' equal to zero and attempt to solve:

Simplifying
-20 + -1x2 = 0

Solving
-20 + -1x2 = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x2 = 0 + 20

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

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

Divide each side by '-1'.
x2 = -20

Simplifying
x2 = -20

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 '(12 + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -1x2 = 0

Solving
12 + -1x2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x2 = 0 + -12
-1x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1x2 = -12

Divide each side by '-1'.
x2 = 12

Simplifying
x2 = 12

Take the square root of each side:
x = {-3.464101615, 3.464101615}
Solution
x = {-3.464101615, 3.464101615}