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

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

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

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

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

Solving for variable 'p'.

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

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

Simplifying
2p + -3q = 0

Solving
2p + -3q = 0

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

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

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

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

Simplifying
p = 1.5q
Subproblem 2
Set the factor '(p + -1q)' equal to zero and attempt to solve:

Simplifying
p + -1q = 0

Solving
p + -1q = 0

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

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

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

Simplifying
p = q
Solution
p = {1.5q, q}