15p^2+pq-2q^2=0

Solution for 15p^2+pq-2q^2=0 equation:

Simplifying
15p2 + pq + -2q2 = 0

Reorder the terms:
pq + 15p2 + -2q2 = 0

Solving
pq + 15p2 + -2q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3p + -1q)(5p + 2q) = 0

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

Simplifying
3p + -1q = 0

Solving
3p + -1q = 0

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

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

Combine like terms: -1q + q = 0
3p + 0 = 0 + q
3p = 0 + q
Remove the zero:
3p = q

Divide each side by '3'.
p = 0.3333333333q

Simplifying
p = 0.3333333333q
Subproblem 2
Set the factor '(5p + 2q)' equal to zero and attempt to solve:

Simplifying
5p + 2q = 0

Solving
5p + 2q = 0

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

Add '-2q' to each side of the equation.
5p + 2q + -2q = 0 + -2q

Combine like terms: 2q + -2q = 0
5p + 0 = 0 + -2q
5p = 0 + -2q
Remove the zero:
5p = -2q

Divide each side by '5'.
p = -0.4q

Simplifying
p = -0.4q
Solution
p = {0.3333333333q, -0.4q}