(n+2)(n+2)=-2n

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

Simplifying
(n + 2)(n + 2) = -2n

Reorder the terms:
(2 + n)(n + 2) = -2n

Reorder the terms:
(2 + n)(2 + n) = -2n

Multiply (2 + n) * (2 + n)
(2(2 + n) + n(2 + n)) = -2n
((2 * 2 + n * 2) + n(2 + n)) = -2n
((4 + 2n) + n(2 + n)) = -2n
(4 + 2n + (2 * n + n * n)) = -2n
(4 + 2n + (2n + n2)) = -2n

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

Solving
4 + 4n + n2 = -2n

Solving for variable 'n'.

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

Combine like terms: 4n + 2n = 6n
4 + 6n + n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
4 + 6n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + 6n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6n + n2 = 0 + -4
6n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
6n + n2 = -4

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = -4 + 9

Reorder the terms:
9 + 6n + n2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + 6n + n2 = 5

Factor a perfect square on the left side:
(n + 3)(n + 3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(n + 3) equal to 2.236067978 and -2.236067978.

Subproblem 1
n + 3 = 2.236067978

Simplifying
n + 3 = 2.236067978

Reorder the terms:
3 + n = 2.236067978

Solving
3 + n = 2.236067978

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = 2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + n = 2.236067978 + -3
n = 2.236067978 + -3

Combine like terms: 2.236067978 + -3 = -0.763932022
n = -0.763932022

Simplifying
n = -0.763932022

Subproblem 2
n + 3 = -2.236067978

Simplifying
n + 3 = -2.236067978

Reorder the terms:
3 + n = -2.236067978

Solving
3 + n = -2.236067978

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = -2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + n = -2.236067978 + -3
n = -2.236067978 + -3

Combine like terms: -2.236067978 + -3 = -5.236067978
n = -5.236067978

Simplifying
n = -5.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.763932022, -5.236067978}