2+2*(n+1)+n*(n+2)=49

Solution for 2+2*(n+1)+n*(n+2)=49 equation:

Simplifying
2 + 2(n + 1) + n(n + 2) = 49

Reorder the terms:
2 + 2(1 + n) + n(n + 2) = 49
2 + (1 * 2 + n * 2) + n(n + 2) = 49
2 + (2 + 2n) + n(n + 2) = 49

Reorder the terms:
2 + 2 + 2n + n(2 + n) = 49
2 + 2 + 2n + (2 * n + n * n) = 49
2 + 2 + 2n + (2n + n2) = 49

Combine like terms: 2 + 2 = 4
4 + 2n + 2n + n2 = 49

Combine like terms: 2n + 2n = 4n
4 + 4n + n2 = 49

Solving
4 + 4n + n2 = 49

Solving for variable 'n'.

Reorder the terms:
4 + -49 + 4n + n2 = 49 + -49

Combine like terms: 4 + -49 = -45
-45 + 4n + n2 = 49 + -49

Combine like terms: 49 + -49 = 0
-45 + 4n + n2 = 0

Factor a trinomial.
(-9 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
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 = {-9, 5}