0=x^4+18x^2-243

Solution for 0=x^4+18x^2-243 equation:

Simplifying
0 = x4 + 18x2 + -243

Reorder the terms:
0 = -243 + 18x2 + x4

Solving
0 = -243 + 18x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 243 = 243
243 + -18x2 + -1x4 = -243 + 18x2 + x4 + 243 + -18x2 + -1x4

Reorder the terms:
243 + -18x2 + -1x4 = -243 + 243 + 18x2 + -18x2 + x4 + -1x4

Combine like terms: -243 + 243 = 0
243 + -18x2 + -1x4 = 0 + 18x2 + -18x2 + x4 + -1x4
243 + -18x2 + -1x4 = 18x2 + -18x2 + x4 + -1x4

Combine like terms: 18x2 + -18x2 = 0
243 + -18x2 + -1x4 = 0 + x4 + -1x4
243 + -18x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
243 + -18x2 + -1x4 = 0

Factor a trinomial.
(9 + -1x2)(27 + x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(27 + x2) = 0

Subproblem 1
Set the factor '(27 + x2)' equal to zero and attempt to solve:

Simplifying
27 + x2 = 0

Solving
27 + x2 = 0

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

Add '-27' to each side of the equation.
27 + -27 + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + x2 = 0 + -27
x2 = 0 + -27

Combine like terms: 0 + -27 = -27
x2 = -27

Simplifying
x2 = -27

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}