-2n(n+7)=-8-n

Solution for -2n(n+7)=-8-n equation:

Simplifying
-2n(n + 7) = -8 + -1n

Reorder the terms:
-2n(7 + n) = -8 + -1n
(7 * -2n + n * -2n) = -8 + -1n
(-14n + -2n2) = -8 + -1n

Solving
-14n + -2n2 = -8 + -1n

Solving for variable 'n'.

Reorder the terms:
8 + -14n + n + -2n2 = -8 + -1n + 8 + n

Combine like terms: -14n + n = -13n
8 + -13n + -2n2 = -8 + -1n + 8 + n

Reorder the terms:
8 + -13n + -2n2 = -8 + 8 + -1n + n

Combine like terms: -8 + 8 = 0
8 + -13n + -2n2 = 0 + -1n + n
8 + -13n + -2n2 = -1n + n

Combine like terms: -1n + n = 0
8 + -13n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4 + 6.5n + n2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6.5n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + 6.5n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6.5n + n2 = 0 + 4
6.5n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
6.5n + n2 = 4

The n term is 6.5n.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5n + 10.5625 + n2 = 4 + 10.5625

Reorder the terms:
10.5625 + 6.5n + n2 = 4 + 10.5625

Combine like terms: 4 + 10.5625 = 14.5625
10.5625 + 6.5n + n2 = 14.5625

Factor a perfect square on the left side:
(n + 3.25)(n + 3.25) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(n + 3.25) equal to 3.816084381 and -3.816084381.

Subproblem 1
n + 3.25 = 3.816084381

Simplifying
n + 3.25 = 3.816084381

Reorder the terms:
3.25 + n = 3.816084381

Solving
3.25 + n = 3.816084381

Solving for variable 'n'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + n = 3.816084381 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + n = 3.816084381 + -3.25
n = 3.816084381 + -3.25

Combine like terms: 3.816084381 + -3.25 = 0.566084381
n = 0.566084381

Simplifying
n = 0.566084381

Subproblem 2
n + 3.25 = -3.816084381

Simplifying
n + 3.25 = -3.816084381

Reorder the terms:
3.25 + n = -3.816084381

Solving
3.25 + n = -3.816084381

Solving for variable 'n'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + n = -3.816084381 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + n = -3.816084381 + -3.25
n = -3.816084381 + -3.25

Combine like terms: -3.816084381 + -3.25 = -7.066084381
n = -7.066084381

Simplifying
n = -7.066084381

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.566084381, -7.066084381}