(x^2)(p^2)+xyp-6y^2=0

Solution for (x^2)(p^2)+xyp-6y^2=0 equation:

Simplifying
(x2)(p2) + xyp + -6y2 = 0

Multiply x2 * p2
p2x2 + xyp + -6y2 = 0

Reorder the terms:
pxy + p2x2 + -6y2 = 0

Solving
pxy + p2x2 + -6y2 = 0

Solving for variable 'p'.

Factor a trinomial.
(px + -2y)(px + 3y) = 0

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

Simplifying
px + -2y = 0

Solving
px + -2y = 0

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

Add '2y' to each side of the equation.
px + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
px + 0 = 0 + 2y
px = 0 + 2y
Remove the zero:
px = 2y

Divide each side by 'x'.
p = 2x-1y

Simplifying
p = 2x-1y
Subproblem 2
Set the factor '(px + 3y)' equal to zero and attempt to solve:

Simplifying
px + 3y = 0

Solving
px + 3y = 0

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

Add '-3y' to each side of the equation.
px + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
px + 0 = 0 + -3y
px = 0 + -3y
Remove the zero:
px = -3y

Divide each side by 'x'.
p = -3x-1y

Simplifying
p = -3x-1y
Solution
p = {2x-1y, -3x-1y}