0=x^4-6x^2-27

Solution for 0=x^4-6x^2-27 equation:

Simplifying
0 = x4 + -6x2 + -27

Reorder the terms:
0 = -27 + -6x2 + x4

Solving
0 = -27 + -6x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 27 = 27
27 + 6x2 + -1x4 = -27 + -6x2 + x4 + 27 + 6x2 + -1x4

Reorder the terms:
27 + 6x2 + -1x4 = -27 + 27 + -6x2 + 6x2 + x4 + -1x4

Combine like terms: -27 + 27 = 0
27 + 6x2 + -1x4 = 0 + -6x2 + 6x2 + x4 + -1x4
27 + 6x2 + -1x4 = -6x2 + 6x2 + x4 + -1x4

Combine like terms: -6x2 + 6x2 = 0
27 + 6x2 + -1x4 = 0 + x4 + -1x4
27 + 6x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
27 + 6x2 + -1x4 = 0

Factor a trinomial.
(9 + -1x2)(3 + x2) = 0

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

Subproblem 1
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 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 + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x2 = 0 + -3
x2 = 0 + -3

Combine like terms: 0 + -3 = -3
x2 = -3

Simplifying
x2 = -3

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}