p(y+x)=

Solution for p(y+x)= equation:

Simplifying
p(y + x) = 0

Reorder the terms:
p(x + y) = 0
(x * p + y * p) = 0
(px + py) = 0

Solving
px + py = 0

Solving for variable 'p'.

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

Factor out the Greatest Common Factor (GCF), 'p'.
p(x + y) = 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 '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

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

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}