6k^2-5kp-6p^2=0

Solution for 6k^2-5kp-6p^2=0 equation:

Simplifying
6k2 + -5kp + -6p2 = 0

Reorder the terms:
-5kp + 6k2 + -6p2 = 0

Solving
-5kp + 6k2 + -6p2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2k + -3p)(3k + 2p) = 0

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

Simplifying
2k + -3p = 0

Solving
2k + -3p = 0

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

Add '3p' to each side of the equation.
2k + -3p + 3p = 0 + 3p

Combine like terms: -3p + 3p = 0
2k + 0 = 0 + 3p
2k = 0 + 3p
Remove the zero:
2k = 3p

Divide each side by '2'.
k = 1.5p

Simplifying
k = 1.5p
Subproblem 2
Set the factor '(3k + 2p)' equal to zero and attempt to solve:

Simplifying
3k + 2p = 0

Solving
3k + 2p = 0

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

Add '-2p' to each side of the equation.
3k + 2p + -2p = 0 + -2p

Combine like terms: 2p + -2p = 0
3k + 0 = 0 + -2p
3k = 0 + -2p
Remove the zero:
3k = -2p

Divide each side by '3'.
k = -0.6666666667p

Simplifying
k = -0.6666666667p
Solution
k = {1.5p, -0.6666666667p}