6r^2+5rp-6p^2=0

Solution for 6r^2+5rp-6p^2=0 equation:

Simplifying
6r2 + 5rp + -6p2 = 0

Reorder the terms:
5pr + -6p2 + 6r2 = 0

Solving
5pr + -6p2 + 6r2 = 0

Solving for variable 'p'.

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

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

Simplifying
-3p + -2r = 0

Solving
-3p + -2r = 0

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

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

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

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

Simplifying
p = -0.6666666667r
Subproblem 2
Set the factor '(2p + -3r)' equal to zero and attempt to solve:

Simplifying
2p + -3r = 0

Solving
2p + -3r = 0

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

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

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

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

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