(n+2)(n+3)=2

Solution for (n+2)(n+3)=2 equation:

Simplifying
(n + 2)(n + 3) = 2

Reorder the terms:
(2 + n)(n + 3) = 2

Reorder the terms:
(2 + n)(3 + n) = 2

Multiply (2 + n) * (3 + n)
(2(3 + n) + n(3 + n)) = 2
((3 * 2 + n * 2) + n(3 + n)) = 2
((6 + 2n) + n(3 + n)) = 2
(6 + 2n + (3 * n + n * n)) = 2
(6 + 2n + (3n + n2)) = 2

Combine like terms: 2n + 3n = 5n
(6 + 5n + n2) = 2

Solving
6 + 5n + n2 = 2

Solving for variable 'n'.

Reorder the terms:
6 + -2 + 5n + n2 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + 5n + n2 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + 5n + n2 = 0

Factor a trinomial.
(4 + n)(1 + n) = 0

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

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

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

Simplifying
n = -4
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

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

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

Simplifying
n = -1
Solution
n = {-4, -1}