(n+1)(n+2)=30

Solution for (n+1)(n+2)=30 equation:

Simplifying
(n + 1)(n + 2) = 30

Reorder the terms:
(1 + n)(n + 2) = 30

Reorder the terms:
(1 + n)(2 + n) = 30

Multiply (1 + n) * (2 + n)
(1(2 + n) + n(2 + n)) = 30
((2 * 1 + n * 1) + n(2 + n)) = 30
((2 + 1n) + n(2 + n)) = 30
(2 + 1n + (2 * n + n * n)) = 30
(2 + 1n + (2n + n2)) = 30

Combine like terms: 1n + 2n = 3n
(2 + 3n + n2) = 30

Solving
2 + 3n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
2 + -30 + 3n + n2 = 30 + -30

Combine like terms: 2 + -30 = -28
-28 + 3n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-28 + 3n + n2 = 0

Factor a trinomial.
(-7 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-7, 4}