16n^2-114n+-14=0

Solution for 16n^2-114n+-14=0 equation:

Simplifying
16n2 + -114n + -14 = 0

Reorder the terms:
-14 + -114n + 16n2 = 0

Solving
-14 + -114n + 16n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -57n + 8n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -57n + 8n2)' equal to zero and attempt to solve:

Simplifying
-7 + -57n + 8n2 = 0

Solving
-7 + -57n + 8n2 = 0

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

Divide each side by '8'.
-0.875 + -7.125n + n2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -7.125n + 0.875 + n2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -7.125n + n2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -7.125n + n2 = 0 + 0.875
-7.125n + n2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-7.125n + n2 = 0.875

The n term is -7.125n.  Take half its coefficient (-3.5625).
Square it (12.69140625) and add it to both sides.

Add '12.69140625' to each side of the equation.
-7.125n + 12.69140625 + n2 = 0.875 + 12.69140625

Reorder the terms:
12.69140625 + -7.125n + n2 = 0.875 + 12.69140625

Combine like terms: 0.875 + 12.69140625 = 13.56640625
12.69140625 + -7.125n + n2 = 13.56640625

Factor a perfect square on the left side:
(n + -3.5625)(n + -3.5625) = 13.56640625

Calculate the square root of the right side: 3.683260275

Break this problem into two subproblems by setting 
(n + -3.5625) equal to 3.683260275 and -3.683260275.

Subproblem 1
n + -3.5625 = 3.683260275

Simplifying
n + -3.5625 = 3.683260275

Reorder the terms:
-3.5625 + n = 3.683260275

Solving
-3.5625 + n = 3.683260275

Solving for variable 'n'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + n = 3.683260275 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + n = 3.683260275 + 3.5625
n = 3.683260275 + 3.5625

Combine like terms: 3.683260275 + 3.5625 = 7.245760275
n = 7.245760275

Simplifying
n = 7.245760275

Subproblem 2
n + -3.5625 = -3.683260275

Simplifying
n + -3.5625 = -3.683260275

Reorder the terms:
-3.5625 + n = -3.683260275

Solving
-3.5625 + n = -3.683260275

Solving for variable 'n'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + n = -3.683260275 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + n = -3.683260275 + 3.5625
n = -3.683260275 + 3.5625

Combine like terms: -3.683260275 + 3.5625 = -0.120760275
n = -0.120760275

Simplifying
n = -0.120760275

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.245760275, -0.120760275}
Solution
n = {7.245760275, -0.120760275}