x^4=3x^2+54

Solution for x^4=3x^2+54 equation:

Simplifying
x4 = 3x2 + 54

Reorder the terms:
x4 = 54 + 3x2

Solving
x4 = 54 + 3x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-6 + -1x2 = 0

Solving
-6 + -1x2 = 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 + -1x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x2 = 0 + 6
-1x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1x2 = 6

Divide each side by '-1'.
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}