K^2X^2-KX-6=0

Solution for K^2X^2-KX-6=0 equation:

Simplifying
K2X2 + -1KX + -6 = 0

Reorder the terms:
-6 + -1KX + K2X2 = 0

Solving
-6 + -1KX + K2X2 = 0

Solving for variable 'K'.

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

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

Simplifying
-2 + -1KX = 0

Solving
-2 + -1KX = 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 + -1KX = 0 + 2

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

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

Divide each side by '-1X'.
K = -2X-1

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

Simplifying
3 + -1KX = 0

Solving
3 + -1KX = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1KX = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1KX = 0 + -3
-1KX = 0 + -3

Combine like terms: 0 + -3 = -3
-1KX = -3

Divide each side by '-1X'.
K = 3X-1

Simplifying
K = 3X-1
Solution
K = {-2X-1, 3X-1}