3x^4-33x^2+72=0

Solution for 3x^4-33x^2+72=0 equation:

Simplifying
3x4 + -33x2 + 72 = 0

Reorder the terms:
72 + -33x2 + 3x4 = 0

Solving
72 + -33x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -11x2 + x4) = 0

Factor a trinomial.
3((3 + -1x2)(8 + -1x2)) = 0

Ignore the factor 3.
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 '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {-1.732050808, 1.732050808, -2.828427125, 2.828427125}