6p^2-pq-12q^2=0

Solution for 6p^2-pq-12q^2=0 equation:

Simplifying
6p2 + -1pq + -12q2 = 0

Reorder the terms:
-1pq + 6p2 + -12q2 = 0

Solving
-1pq + 6p2 + -12q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(2p + -3q)(3p + 4q) = 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 '(3p + 4q)' equal to zero and attempt to solve:

Simplifying
3p + 4q = 0

Solving
3p + 4q = 0

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

Add '-4q' to each side of the equation.
3p + 4q + -4q = 0 + -4q

Combine like terms: 4q + -4q = 0
3p + 0 = 0 + -4q
3p = 0 + -4q
Remove the zero:
3p = -4q

Divide each side by '3'.
p = -1.333333333q

Simplifying
p = -1.333333333q
Solution
p = {1.5q, -1.333333333q}