n(n+2)+n+2=12

Solution for n(n+2)+n+2=12 equation:

Simplifying
n(n + 2) + n + 2 = 12

Reorder the terms:
n(2 + n) + n + 2 = 12
(2 * n + n * n) + n + 2 = 12
(2n + n2) + n + 2 = 12

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

Combine like terms: 2n + n = 3n
2 + 3n + n2 = 12

Solving
2 + 3n + n2 = 12

Solving for variable 'n'.

Reorder the terms:
2 + -12 + 3n + n2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 3n + n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 3n + n2 = 0

Factor a trinomial.
(-5 + -1n)(2 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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