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.
(3k + -2p)(2k + 3p) = 0

Subproblem 1
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
Subproblem 2
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
Solution
k = {0.6666666667p, -1.5p}