x^4+6x^2=27

Solution for x^4+6x^2=27 equation:

Simplifying
x4 + 6x2 = 27

Reorder the terms:
6x2 + x4 = 27

Solving
6x2 + x4 = 27

Solving for variable 'x'.

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

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

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

Subproblem 1
Set the factor '(-9 + -1x2)' equal to zero and attempt to solve:

Simplifying
-9 + -1x2 = 0

Solving
-9 + -1x2 = 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 + -1x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x2 = 0 + 9
-1x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1x2 = 9

Divide each side by '-1'.
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.
Subproblem 2
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}
Solution
x = {-1.732050808, 1.732050808}