(p+5)(p+3)=0

Solution for (p+5)(p+3)=0 equation:

Simplifying
(p + 5)(p + 3) = 0

Reorder the terms:
(5 + p)(p + 3) = 0

Reorder the terms:
(5 + p)(3 + p) = 0

Multiply (5 + p) * (3 + p)
(5(3 + p) + p(3 + p)) = 0
((3 * 5 + p * 5) + p(3 + p)) = 0
((15 + 5p) + p(3 + p)) = 0
(15 + 5p + (3 * p + p * p)) = 0
(15 + 5p + (3p + p2)) = 0

Combine like terms: 5p + 3p = 8p
(15 + 8p + p2) = 0

Solving
15 + 8p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(5 + p)(3 + p) = 0

Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 0

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

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

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

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

Simplifying
p = -5
Subproblem 2
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

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

Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Solution
p = {-5, -3}