6x^4-216=0

Solution for 6x^4-216=0 equation:

Simplifying
6x4 + -216 = 0

Reorder the terms:
-216 + 6x4 = 0

Solving
-216 + 6x4 = 0

Solving for variable 'x'.

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

Add '216' to each side of the equation.
-216 + 216 + 6x4 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + 6x4 = 0 + 216
6x4 = 0 + 216

Combine like terms: 0 + 216 = 216
6x4 = 216

Divide each side by '6'.
x4 = 36

Simplifying
x4 = 36

Reorder the terms:
-36 + x4 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + x4 = 0

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

Subproblem 1
Set the factor '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

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

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

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

Simplifying
x2 = -6

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

Simplifying
-6 + x2 = 0

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

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

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

Simplifying
x2 = 6

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