14p^2+23pq+3q^2=0

Solution for 14p^2+23pq+3q^2=0 equation:

Simplifying
14p2 + 23pq + 3q2 = 0

Reorder the terms:
23pq + 14p2 + 3q2 = 0

Solving
23pq + 14p2 + 3q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(7p + q)(2p + 3q) = 0

Subproblem 1
Set the factor '(7p + q)' equal to zero and attempt to solve:

Simplifying
7p + q = 0

Solving
7p + q = 0

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

Add '-1q' to each side of the equation.
7p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
7p + 0 = 0 + -1q
7p = 0 + -1q
Remove the zero:
7p = -1q

Divide each side by '7'.
p = -0.1428571429q

Simplifying
p = -0.1428571429q
Subproblem 2
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
Solution
p = {-0.1428571429q, -1.5q}