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

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

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

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

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

Solving for variable 'p'.

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

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

Simplifying
2p + -1q = 0

Solving
2p + -1q = 0

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

Add 'q' to each side of the equation.
2p + -1q + q = 0 + q

Combine like terms: -1q + q = 0
2p + 0 = 0 + q
2p = 0 + q
Remove the zero:
2p = q

Divide each side by '2'.
p = 0.5q

Simplifying
p = 0.5q
Subproblem 2
Set the factor '(3p + q)' equal to zero and attempt to solve:

Simplifying
3p + q = 0

Solving
3p + q = 0

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

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

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

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

Simplifying
p = -0.3333333333q
Solution
p = {0.5q, -0.3333333333q}