33x^2-4x^4+27=0

Solution for 33x^2-4x^4+27=0 equation:

Simplifying
33x2 + -4x4 + 27 = 0

Reorder the terms:
27 + 33x2 + -4x4 = 0

Solving
27 + 33x2 + -4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(3 + 4x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(3 + 4x2) = 0

Subproblem 1
Set the factor '(3 + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x2 = 0

Solving
3 + 4x2 = 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 + 4x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x2 = 0 + -3
4x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4x2 = -3

Divide each side by '4'.
x2 = -0.75

Simplifying
x2 = -0.75

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}