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

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

Simplifying
2q2 + -1pq + -1p2 = 0

Reorder the terms:
-1pq + -1p2 + 2q2 = 0

Solving
-1pq + -1p2 + 2q2 = 0

Solving for variable 'p'.

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

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

Simplifying
-1p + -2q = 0

Solving
-1p + -2q = 0

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

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

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

Divide each side by '-1'.
p = -2q

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