p(r+s)=

Solution for p(r+s)= equation:

Simplifying
p(r + s) = 0
(r * p + s * p) = 0
(pr + ps) = 0

Solving
pr + ps = 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(r + s) = 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 '(r + s)' equal to zero and attempt to solve:

Simplifying
r + s = 0

Solving
r + s = 0

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

Add '-1r' to each side of the equation.
r + -1r + s = 0 + -1r

Combine like terms: r + -1r = 0
0 + s = 0 + -1r
s = 0 + -1r
Remove the zero:
s = -1r

Add '-1s' to each side of the equation.
s + -1s = -1r + -1s

Combine like terms: s + -1s = 0
0 = -1r + -1s

Simplifying
0 = -1r + -1s

The solution to this equation could not be determined.

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