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.
(3 + -1x2)(9 + x2) = 0

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

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.732050808, 1.732050808}