(12k^4)+(5k^2)-2=0

Solution for (12k^4)+(5k^2)-2=0 equation:

Simplifying
(12k4) + (5k2) + -2 = 0

Reorder the terms:
-2 + (5k2) + (12k4) = 0

Solving
-2 + (5k2) + (12k4) = 0

Solving for variable 'k'.

Factor a trinomial.
(-2 + -3k2)(1 + -4k2) = 0

Factor a difference between two squares.
(-2 + -3k2)((1 + 2k)(1 + -2k)) = 0

Subproblem 1
Set the factor '(-2 + -3k2)' equal to zero and attempt to solve:

Simplifying
-2 + -3k2 = 0

Solving
-2 + -3k2 = 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 + -3k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k2 = 0 + 2
-3k2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3k2 = 2

Divide each side by '-3'.
k2 = -0.6666666667

Simplifying
k2 = -0.6666666667

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 '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

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

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

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

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 3
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

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

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-0.5, 0.5}