-4n^2+2n+16=0

Solution for -4n^2+2n+16=0 equation:

Simplifying
-4n2 + 2n + 16 = 0

Reorder the terms:
16 + 2n + -4n2 = 0

Solving
16 + 2n + -4n2 = 0

Solving for variable 'n'.

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

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

Simplifying
8 + n + -2n2 = 0

Solving
8 + n + -2n2 = 0

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

Divide each side by '-2'.
-4 + -0.5n + n2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.5n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.5n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.5n + n2 = 0 + 4
-0.5n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.5n + n2 = 4

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 = 4 + 0.25

Reorder the terms:
0.25 + -0.5n + n2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -0.5n + n2 = 4.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(n + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
n + 0.5 = 2.061552813

Simplifying
n + 0.5 = 2.061552813

Reorder the terms:
0.5 + n = 2.061552813

Solving
0.5 + n = 2.061552813

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 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 2.061552813 + -0.5
n = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
n = 1.561552813

Simplifying
n = 1.561552813

Subproblem 2
n + 0.5 = -2.061552813

Simplifying
n + 0.5 = -2.061552813

Reorder the terms:
0.5 + n = -2.061552813

Solving
0.5 + n = -2.061552813

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 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -2.061552813 + -0.5
n = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
n = -2.561552813

Simplifying
n = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.561552813, -2.561552813}
Solution
n = {1.561552813, -2.561552813}