(p+2)(p+3)=1-p

Solution for (p+2)(p+3)=1-p equation:

Simplifying
(p + 2)(p + 3) = 1 + -1p

Reorder the terms:
(2 + p)(p + 3) = 1 + -1p

Reorder the terms:
(2 + p)(3 + p) = 1 + -1p

Multiply (2 + p) * (3 + p)
(2(3 + p) + p(3 + p)) = 1 + -1p
((3 * 2 + p * 2) + p(3 + p)) = 1 + -1p
((6 + 2p) + p(3 + p)) = 1 + -1p
(6 + 2p + (3 * p + p * p)) = 1 + -1p
(6 + 2p + (3p + p2)) = 1 + -1p

Combine like terms: 2p + 3p = 5p
(6 + 5p + p2) = 1 + -1p

Solving
6 + 5p + p2 = 1 + -1p

Solving for variable 'p'.

Reorder the terms:
6 + -1 + 5p + p + p2 = 1 + -1p + -1 + p

Combine like terms: 6 + -1 = 5
5 + 5p + p + p2 = 1 + -1p + -1 + p

Combine like terms: 5p + p = 6p
5 + 6p + p2 = 1 + -1p + -1 + p

Reorder the terms:
5 + 6p + p2 = 1 + -1 + -1p + p

Combine like terms: 1 + -1 = 0
5 + 6p + p2 = 0 + -1p + p
5 + 6p + p2 = -1p + p

Combine like terms: -1p + p = 0
5 + 6p + p2 = 0

Factor a trinomial.
(5 + p)(1 + 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 '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1

Combine like terms: 0 + -1 = -1
p = -1

Simplifying
p = -1
Solution
p = {-5, -1}