3p^2+5pq-2q^2=0

Solution for 3p^2+5pq-2q^2=0 equation:

Simplifying
3p2 + 5pq + -2q2 = 0

Reorder the terms:
5pq + 3p2 + -2q2 = 0

Solving
5pq + 3p2 + -2q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3p + -1q)(p + 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 '(p + 2q)' equal to zero and attempt to solve:

Simplifying
p + 2q = 0

Solving
p + 2q = 0

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

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

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

Simplifying
p = -2q
Solution
p = {0.3333333333q, -2q}