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

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

Simplifying
2 + 2(n + 1) + n(n + 2) = 0

Reorder the terms:
2 + 2(1 + n) + n(n + 2) = 0
2 + (1 * 2 + n * 2) + n(n + 2) = 0
2 + (2 + 2n) + n(n + 2) = 0

Reorder the terms:
2 + 2 + 2n + n(2 + n) = 0
2 + 2 + 2n + (2 * n + n * n) = 0
2 + 2 + 2n + (2n + n2) = 0

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

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

Solving
4 + 4n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + n)(2 + n) = 0

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

Simplifying
2 + n = 0

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

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

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

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

Simplifying
2 + n = 0

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

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

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

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