(n+3)(n+4)=2

Solution for (n+3)(n+4)=2 equation:

Simplifying
(n + 3)(n + 4) = 2

Reorder the terms:
(3 + n)(n + 4) = 2

Reorder the terms:
(3 + n)(4 + n) = 2

Multiply (3 + n) * (4 + n)
(3(4 + n) + n(4 + n)) = 2
((4 * 3 + n * 3) + n(4 + n)) = 2
((12 + 3n) + n(4 + n)) = 2
(12 + 3n + (4 * n + n * n)) = 2
(12 + 3n + (4n + n2)) = 2

Combine like terms: 3n + 4n = 7n
(12 + 7n + n2) = 2

Solving
12 + 7n + n2 = 2

Solving for variable 'n'.

Reorder the terms:
12 + -2 + 7n + n2 = 2 + -2

Combine like terms: 12 + -2 = 10
10 + 7n + n2 = 2 + -2

Combine like terms: 2 + -2 = 0
10 + 7n + n2 = 0

Factor a trinomial.
(5 + n)(2 + n) = 0

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

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

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

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

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-5, -2}