pm^2+9pm+20p=0

Solution for pm^2+9pm+20p=0 equation:

Simplifying
pm2 + 9pm + 20p = 0

Reorder the terms:
9mp + m2p + 20p = 0

Solving
9mp + m2p + 20p = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(9m + m2 + 20) = 0

Factor a trinomial.
p((m + 4)(m + 5)) = 0

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

Simplifying
p = 0

Solving
p = 0

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

Add '-1p' to each side of the equation.
p + -1p = 0 + -1p
Remove the zero:
0 = -1p

Simplifying
0 = -1p

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(m + 4)' equal to zero and attempt to solve:

Simplifying
m + 4 = 0

Reorder the terms:
4 + m = 0

Solving
4 + m = 0

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

Add '-4' to each side of the equation.
4 + -4 + m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + m = 0 + -4
m = 0 + -4

Combine like terms: 0 + -4 = -4
m = -4

Simplifying
m = -4
Subproblem 3
Set the factor '(m + 5)' equal to zero and attempt to solve:

Simplifying
m + 5 = 0

Reorder the terms:
5 + m = 0

Solving
5 + m = 0

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

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

Combine like terms: 5 + -5 = 0
0 + m = 0 + -5
m = 0 + -5

Combine like terms: 0 + -5 = -5
m = -5

Simplifying
m = -5
Solution
m = {-4, -5}