xp^2+yp=0

Solution for xp^2+yp=0 equation:

Simplifying
xp2 + yp = 0

Reorder the terms:
py + p2x = 0

Solving
py + p2x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(y + px) = 0

Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(y + px)' equal to zero and attempt to solve:

Simplifying
y + px = 0

Reorder the terms:
px + y = 0

Solving
px + y = 0

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

Add '-1y' to each side of the equation.
px + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
px + 0 = 0 + -1y
px = 0 + -1y
Remove the zero:
px = -1y

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

Simplifying
p = -1x-1y
Solution
p = {0, -1x-1y}