0=2x^4-4x^2-48

Solution for 0=2x^4-4x^2-48 equation:

Simplifying
0 = 2x4 + -4x2 + -48

Reorder the terms:
0 = -48 + -4x2 + 2x4

Solving
0 = -48 + -4x2 + 2x4

Solving for variable 'x'.

Combine like terms: 0 + 48 = 48
48 + 4x2 + -2x4 = -48 + -4x2 + 2x4 + 48 + 4x2 + -2x4

Reorder the terms:
48 + 4x2 + -2x4 = -48 + 48 + -4x2 + 4x2 + 2x4 + -2x4

Combine like terms: -48 + 48 = 0
48 + 4x2 + -2x4 = 0 + -4x2 + 4x2 + 2x4 + -2x4
48 + 4x2 + -2x4 = -4x2 + 4x2 + 2x4 + -2x4

Combine like terms: -4x2 + 4x2 = 0
48 + 4x2 + -2x4 = 0 + 2x4 + -2x4
48 + 4x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
48 + 4x2 + -2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 2x2 + -1x4) = 0

Factor a trinomial.
2((6 + -1x2)(4 + x2)) = 0

Ignore the factor 2.
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

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(4 + x2)' equal to zero and attempt to solve:

Simplifying
4 + x2 = 0

Solving
4 + x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + x2 = 0 + -4

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

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

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.449489743, 2.449489743}