x^4+6x^2-72=0

Solution for x^4+6x^2-72=0 equation:

Simplifying
x4 + 6x2 + -72 = 0

Reorder the terms:
-72 + 6x2 + x4 = 0

Solving
-72 + 6x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x2)(6 + -1x2) = 0

Subproblem 1
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

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

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 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 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-2.449489743, 2.449489743}