0=x^4-3x^2-54

Solution for 0=x^4-3x^2-54 equation:

Simplifying
0 = x4 + -3x2 + -54

Reorder the terms:
0 = -54 + -3x2 + x4

Solving
0 = -54 + -3x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + 3x2 + -1x4 = -54 + -3x2 + x4 + 54 + 3x2 + -1x4

Reorder the terms:
54 + 3x2 + -1x4 = -54 + 54 + -3x2 + 3x2 + x4 + -1x4

Combine like terms: -54 + 54 = 0
54 + 3x2 + -1x4 = 0 + -3x2 + 3x2 + x4 + -1x4
54 + 3x2 + -1x4 = -3x2 + 3x2 + x4 + -1x4

Combine like terms: -3x2 + 3x2 = 0
54 + 3x2 + -1x4 = 0 + x4 + -1x4
54 + 3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
54 + 3x2 + -1x4 = 0

Factor a trinomial.
(9 + -1x2)(6 + x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(6 + x2) = 0

Subproblem 1
Set the factor '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 0 + -6

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

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

Simplifying
x2 = -6

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}