p(p+12)=-32

Solution for p(p+12)=-32 equation:

Simplifying
p(p + 12) = -32

Reorder the terms:
p(12 + p) = -32
(12 * p + p * p) = -32
(12p + p2) = -32

Solving
12p + p2 = -32

Solving for variable 'p'.

Reorder the terms:
32 + 12p + p2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + 12p + p2 = 0

Factor a trinomial.
(8 + p)(4 + p) = 0

Subproblem 1
Set the factor '(8 + p)' equal to zero and attempt to solve:

Simplifying
8 + p = 0

Solving
8 + p = 0

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

Add '-8' to each side of the equation.
8 + -8 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 0

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

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

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

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

Simplifying
p = -4
Solution
p = {-8, -4}