55=(x^2-2)(x^2+4)

Solution for 55=(x^2-2)(x^2+4) equation:

Simplifying
55 = (x2 + -2)(x2 + 4)

Reorder the terms:
55 = (-2 + x2)(x2 + 4)

Reorder the terms:
55 = (-2 + x2)(4 + x2)

Multiply (-2 + x2) * (4 + x2)
55 = (-2(4 + x2) + x2(4 + x2))
55 = ((4 * -2 + x2 * -2) + x2(4 + x2))
55 = ((-8 + -2x2) + x2(4 + x2))
55 = (-8 + -2x2 + (4 * x2 + x2 * x2))
55 = (-8 + -2x2 + (4x2 + x4))

Combine like terms: -2x2 + 4x2 = 2x2
55 = (-8 + 2x2 + x4)

Solving
55 = -8 + 2x2 + x4

Solving for variable 'x'.

Combine like terms: 55 + 8 = 63
63 + -2x2 + -1x4 = -8 + 2x2 + x4 + 8 + -2x2 + -1x4

Reorder the terms:
63 + -2x2 + -1x4 = -8 + 8 + 2x2 + -2x2 + x4 + -1x4

Combine like terms: -8 + 8 = 0
63 + -2x2 + -1x4 = 0 + 2x2 + -2x2 + x4 + -1x4
63 + -2x2 + -1x4 = 2x2 + -2x2 + x4 + -1x4

Combine like terms: 2x2 + -2x2 = 0
63 + -2x2 + -1x4 = 0 + x4 + -1x4
63 + -2x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
63 + -2x2 + -1x4 = 0

Factor a trinomial.
(7 + -1x2)(9 + x2) = 0

Subproblem 1
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

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

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

Combine like terms: 0 + -9 = -9
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.
Solution
x = {-2.645751311, 2.645751311}