-0.5(n+2)(n+2)=0

Solution for -0.5(n+2)(n+2)=0 equation:

Simplifying
-0.5(n + 2)(n + 2) = 0

Reorder the terms:
-0.5(2 + n)(n + 2) = 0

Reorder the terms:
-0.5(2 + n)(2 + n) = 0

Multiply (2 + n) * (2 + n)
-0.5(2(2 + n) + n(2 + n)) = 0
-0.5((2 * 2 + n * 2) + n(2 + n)) = 0
-0.5((4 + 2n) + n(2 + n)) = 0
-0.5(4 + 2n + (2 * n + n * n)) = 0
-0.5(4 + 2n + (2n + n2)) = 0

Combine like terms: 2n + 2n = 4n
-0.5(4 + 4n + n2) = 0
(4 * -0.5 + 4n * -0.5 + n2 * -0.5) = 0
(-2 + -2n + -0.5n2) = 0

Solving
-2 + -2n + -0.5n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
4 + 4n + n2 = 0

Move the constant term to the right:

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

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

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

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

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

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

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

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

Factor a perfect square on the left side:
(n + 2)(n + 2) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(n + 2) equal to 0 and 0.

Subproblem 1
n + 2 = 0

Simplifying
n + 2 = 0

Reorder the terms:
2 + n = 0

Solving
2 + n = 0

Solving for variable 'n'.

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
n + 2 = 0

Simplifying
n + 2 = 0

Reorder the terms:
2 + n = 0

Solving
2 + n = 0

Solving for variable 'n'.

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
The solution to the problem is based on the solutions
from the subproblems.
n = {-2, -2}