n(n+2)=11+2(n+n+2)

Solution for n(n+2)=11+2(n+n+2) equation:

Simplifying
n(n + 2) = 11 + 2(n + n + 2)

Reorder the terms:
n(2 + n) = 11 + 2(n + n + 2)
(2 * n + n * n) = 11 + 2(n + n + 2)
(2n + n2) = 11 + 2(n + n + 2)

Reorder the terms:
2n + n2 = 11 + 2(2 + n + n)

Combine like terms: n + n = 2n
2n + n2 = 11 + 2(2 + 2n)
2n + n2 = 11 + (2 * 2 + 2n * 2)
2n + n2 = 11 + (4 + 4n)

Combine like terms: 11 + 4 = 15
2n + n2 = 15 + 4n

Solving
2n + n2 = 15 + 4n

Solving for variable 'n'.

Reorder the terms:
-15 + 2n + -4n + n2 = 15 + 4n + -15 + -4n

Combine like terms: 2n + -4n = -2n
-15 + -2n + n2 = 15 + 4n + -15 + -4n

Reorder the terms:
-15 + -2n + n2 = 15 + -15 + 4n + -4n

Combine like terms: 15 + -15 = 0
-15 + -2n + n2 = 0 + 4n + -4n
-15 + -2n + n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-15 + -2n + n2 = 0

Factor a trinomial.
(-3 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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 = {-3, 5}