12x^4-192=0

Solution for 12x^4-192=0 equation:

Simplifying
12x4 + -192 = 0

Reorder the terms:
-192 + 12x4 = 0

Solving
-192 + 12x4 = 0

Solving for variable 'x'.

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

Add '192' to each side of the equation.
-192 + 192 + 12x4 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 12x4 = 0 + 192
12x4 = 0 + 192

Combine like terms: 0 + 192 = 192
12x4 = 192

Divide each side by '12'.
x4 = 16

Simplifying
x4 = 16

Reorder the terms:
-16 + x4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + x4 = 0

Factor a difference between two squares.
(4 + x2)(-4 + x2) = 0

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

Subproblem 1
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.
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 + 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
Solution
x = {-2, 2}