x^4-68x^2-288=0

Solution for x^4-68x^2-288=0 equation:

Simplifying
x4 + -68x2 + -288 = 0

Reorder the terms:
-288 + -68x2 + x4 = 0

Solving
-288 + -68x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x2)(72 + -1x2) = 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 '(72 + -1x2)' equal to zero and attempt to solve:

Simplifying
72 + -1x2 = 0

Solving
72 + -1x2 = 0

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

Add '-72' to each side of the equation.
72 + -72 + -1x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -1x2 = 0 + -72
-1x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-1x2 = -72

Divide each side by '-1'.
x2 = 72

Simplifying
x2 = 72

Take the square root of each side:
x = {-8.485281374, 8.485281374}
Solution
x = {-8.485281374, 8.485281374}