(p+9)(p+3)=-8

Solution for (p+9)(p+3)=-8 equation:

Simplifying
(p + 9)(p + 3) = -8

Reorder the terms:
(9 + p)(p + 3) = -8

Reorder the terms:
(9 + p)(3 + p) = -8

Multiply (9 + p) * (3 + p)
(9(3 + p) + p(3 + p)) = -8
((3 * 9 + p * 9) + p(3 + p)) = -8
((27 + 9p) + p(3 + p)) = -8
(27 + 9p + (3 * p + p * p)) = -8
(27 + 9p + (3p + p2)) = -8

Combine like terms: 9p + 3p = 12p
(27 + 12p + p2) = -8

Solving
27 + 12p + p2 = -8

Solving for variable 'p'.

Reorder the terms:
27 + 8 + 12p + p2 = -8 + 8

Combine like terms: 27 + 8 = 35
35 + 12p + p2 = -8 + 8

Combine like terms: -8 + 8 = 0
35 + 12p + p2 = 0

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

Subproblem 1
Set the factor '(7 + p)' equal to zero and attempt to solve:

Simplifying
7 + p = 0

Solving
7 + p = 0

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

Add '-7' to each side of the equation.
7 + -7 + p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + p = 0 + -7
p = 0 + -7

Combine like terms: 0 + -7 = -7
p = -7

Simplifying
p = -7
Subproblem 2
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
Solution
p = {-7, -5}