5n(n+8)+4(-4+4n)=

Solution for 5n(n+8)+4(-4+4n)= equation:

Simplifying
5n(n + 8) + 4(-4 + 4n) = 0

Reorder the terms:
5n(8 + n) + 4(-4 + 4n) = 0
(8 * 5n + n * 5n) + 4(-4 + 4n) = 0
(40n + 5n2) + 4(-4 + 4n) = 0
40n + 5n2 + (-4 * 4 + 4n * 4) = 0
40n + 5n2 + (-16 + 16n) = 0

Reorder the terms:
-16 + 40n + 16n + 5n2 = 0

Combine like terms: 40n + 16n = 56n
-16 + 56n + 5n2 = 0

Solving
-16 + 56n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
-3.2 + 11.2n + n2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 11.2n + 3.2 + n2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 11.2n + n2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 11.2n + n2 = 0 + 3.2
11.2n + n2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
11.2n + n2 = 3.2

The n term is 11.2n.  Take half its coefficient (5.6).
Square it (31.36) and add it to both sides.

Add '31.36' to each side of the equation.
11.2n + 31.36 + n2 = 3.2 + 31.36

Reorder the terms:
31.36 + 11.2n + n2 = 3.2 + 31.36

Combine like terms: 3.2 + 31.36 = 34.56
31.36 + 11.2n + n2 = 34.56

Factor a perfect square on the left side:
(n + 5.6)(n + 5.6) = 34.56

Calculate the square root of the right side: 5.878775383

Break this problem into two subproblems by setting 
(n + 5.6) equal to 5.878775383 and -5.878775383.

Subproblem 1
n + 5.6 = 5.878775383

Simplifying
n + 5.6 = 5.878775383

Reorder the terms:
5.6 + n = 5.878775383

Solving
5.6 + n = 5.878775383

Solving for variable 'n'.

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

Add '-5.6' to each side of the equation.
5.6 + -5.6 + n = 5.878775383 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
0.0 + n = 5.878775383 + -5.6
n = 5.878775383 + -5.6

Combine like terms: 5.878775383 + -5.6 = 0.278775383
n = 0.278775383

Simplifying
n = 0.278775383

Subproblem 2
n + 5.6 = -5.878775383

Simplifying
n + 5.6 = -5.878775383

Reorder the terms:
5.6 + n = -5.878775383

Solving
5.6 + n = -5.878775383

Solving for variable 'n'.

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

Add '-5.6' to each side of the equation.
5.6 + -5.6 + n = -5.878775383 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
0.0 + n = -5.878775383 + -5.6
n = -5.878775383 + -5.6

Combine like terms: -5.878775383 + -5.6 = -11.478775383
n = -11.478775383

Simplifying
n = -11.478775383

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.278775383, -11.478775383}