5p^2r+p^2=0

Solution for 5p^2r+p^2=0 equation:

Simplifying
5p2r + p2 = 0

Reorder the terms:
p2 + 5p2r = 0

Solving
p2 + 5p2r = 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), 'p2'.
p2(1 + 5r) = 0

Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

Take the square root of each side:
p = {0}
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5r = 0 + -1
5r = 0 + -1

Combine like terms: 0 + -1 = -1
5r = -1

Add '-5r' to each side of the equation.
5r + -5r = -1 + -5r

Combine like terms: 5r + -5r = 0
0 = -1 + -5r

Simplifying
0 = -1 + -5r

The solution to this equation could not be determined.

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