x^4+8x^2-48=0

Solution for x^4+8x^2-48=0 equation:

Simplifying
x4 + 8x2 + -48 = 0

Reorder the terms:
-48 + 8x2 + x4 = 0

Solving
-48 + 8x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-12 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-12 + -1x2)' equal to zero and attempt to solve:

Simplifying
-12 + -1x2 = 0

Solving
-12 + -1x2 = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x2 = 0 + 12
-1x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1x2 = 12

Divide each side by '-1'.
x2 = -12

Simplifying
x2 = -12

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}