16n^2+8n-896=0

Solution for 16n^2+8n-896=0 equation:

Simplifying
16n2 + 8n + -896 = 0

Reorder the terms:
-896 + 8n + 16n2 = 0

Solving
-896 + 8n + 16n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-112 + n + 2n2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-112 + n + 2n2)' equal to zero and attempt to solve:

Simplifying
-112 + n + 2n2 = 0

Solving
-112 + n + 2n2 = 0

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

Divide each side by '2'.
-56 + 0.5n + n2 = 0

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 0.5n + 56 + n2 = 0 + 56

Reorder the terms:
-56 + 56 + 0.5n + n2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 0.5n + n2 = 0 + 56
0.5n + n2 = 0 + 56

Combine like terms: 0 + 56 = 56
0.5n + n2 = 56

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.
0.5n + 0.25 + n2 = 56 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = 56 + 0.25

Combine like terms: 56 + 0.25 = 56.25
0.25 + 0.5n + n2 = 56.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 56.25

Calculate the square root of the right side: 7.5

Break this problem into two subproblems by setting 
(n + 0.5) equal to 7.5 and -7.5.

Subproblem 1
n + 0.5 = 7.5

Simplifying
n + 0.5 = 7.5

Reorder the terms:
0.5 + n = 7.5

Solving
0.5 + n = 7.5

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 = 7.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 7.5 + -0.5
n = 7.5 + -0.5

Combine like terms: 7.5 + -0.5 = 7
n = 7

Simplifying
n = 7

Subproblem 2
n + 0.5 = -7.5

Simplifying
n + 0.5 = -7.5

Reorder the terms:
0.5 + n = -7.5

Solving
0.5 + n = -7.5

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 = -7.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -7.5 + -0.5
n = -7.5 + -0.5

Combine like terms: -7.5 + -0.5 = -8
n = -8

Simplifying
n = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7, -8}
Solution
n = {7, -8}