-8n(4+n)+3(3+8n)=

Solution for -8n(4+n)+3(3+8n)= equation:

Simplifying
-8n(4 + n) + 3(3 + 8n) = 0
(4 * -8n + n * -8n) + 3(3 + 8n) = 0
(-32n + -8n2) + 3(3 + 8n) = 0
-32n + -8n2 + (3 * 3 + 8n * 3) = 0
-32n + -8n2 + (9 + 24n) = 0

Reorder the terms:
9 + -32n + 24n + -8n2 = 0

Combine like terms: -32n + 24n = -8n
9 + -8n + -8n2 = 0

Solving
9 + -8n + -8n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.125 + n + n2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + n + 1.125 + n2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + n + n2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + n + n2 = 0 + 1.125
n + n2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
n + n2 = 1.125

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + n2 = 1.125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 1.125 + 0.25

Combine like terms: 1.125 + 0.25 = 1.375
1.25 + n2 = 1.375

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 1.375

Calculate the square root of the right side: 1.17260394

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.17260394 and -1.17260394.

Subproblem 1
n + 0.5 = 1.17260394

Simplifying
n + 0.5 = 1.17260394

Reorder the terms:
0.5 + n = 1.17260394

Solving
0.5 + n = 1.17260394

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 1.17260394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 1.17260394 + -0.5
n = 1.17260394 + -0.5

Combine like terms: 1.17260394 + -0.5 = 0.67260394
n = 0.67260394

Simplifying
n = 0.67260394

Subproblem 2
n + 0.5 = -1.17260394

Simplifying
n + 0.5 = -1.17260394

Reorder the terms:
0.5 + n = -1.17260394

Solving
0.5 + n = -1.17260394

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -1.17260394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -1.17260394 + -0.5
n = -1.17260394 + -0.5

Combine like terms: -1.17260394 + -0.5 = -1.67260394
n = -1.67260394

Simplifying
n = -1.67260394

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.67260394, -1.67260394}