K^4-4K^2-12=0

Solution for K^4-4K^2-12=0 equation:

Simplifying
K4 + -4K2 + -12 = 0

Reorder the terms:
-12 + -4K2 + K4 = 0

Solving
-12 + -4K2 + K4 = 0

Solving for variable 'K'.

Factor a trinomial.
(-2 + -1K2)(6 + -1K2) = 0

Subproblem 1
Set the factor '(-2 + -1K2)' equal to zero and attempt to solve:

Simplifying
-2 + -1K2 = 0

Solving
-2 + -1K2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1K2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1K2 = 0 + 2
-1K2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1K2 = 2

Divide each side by '-1'.
K2 = -2

Simplifying
K2 = -2

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 '(6 + -1K2)' equal to zero and attempt to solve:

Simplifying
6 + -1K2 = 0

Solving
6 + -1K2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1K2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1K2 = 0 + -6
-1K2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1K2 = -6

Divide each side by '-1'.
K2 = 6

Simplifying
K2 = 6

Take the square root of each side:
K = {-2.449489743, 2.449489743}
Solution
K = {-2.449489743, 2.449489743}