(n+1)(n+2)=42

Solution for (n+1)(n+2)=42 equation:

Simplifying
(n + 1)(n + 2) = 42

Reorder the terms:
(1 + n)(n + 2) = 42

Reorder the terms:
(1 + n)(2 + n) = 42

Multiply (1 + n) * (2 + n)
(1(2 + n) + n(2 + n)) = 42
((2 * 1 + n * 1) + n(2 + n)) = 42
((2 + 1n) + n(2 + n)) = 42
(2 + 1n + (2 * n + n * n)) = 42
(2 + 1n + (2n + n2)) = 42

Combine like terms: 1n + 2n = 3n
(2 + 3n + n2) = 42

Solving
2 + 3n + n2 = 42

Solving for variable 'n'.

Reorder the terms:
2 + -42 + 3n + n2 = 42 + -42

Combine like terms: 2 + -42 = -40
-40 + 3n + n2 = 42 + -42

Combine like terms: 42 + -42 = 0
-40 + 3n + n2 = 0

Factor a trinomial.
(-8 + -1n)(5 + -1n) = 0

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

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-8, 5}