10n^2+4n-16=0

Solution for 10n^2+4n-16=0 equation:

Simplifying
10n2 + 4n + -16 = 0

Reorder the terms:
-16 + 4n + 10n2 = 0

Solving
-16 + 4n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 2n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 2n + 5n2)' equal to zero and attempt to solve:

Simplifying
-8 + 2n + 5n2 = 0

Solving
-8 + 2n + 5n2 = 0

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

Divide each side by '5'.
-1.6 + 0.4n + n2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.4n + 1.6 + n2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.4n + n2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.4n + n2 = 0 + 1.6
0.4n + n2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.4n + n2 = 1.6

The n term is 0.4n.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4n + 0.04 + n2 = 1.6 + 0.04

Reorder the terms:
0.04 + 0.4n + n2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + 0.4n + n2 = 1.64

Factor a perfect square on the left side:
(n + 0.2)(n + 0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(n + 0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
n + 0.2 = 1.280624847

Simplifying
n + 0.2 = 1.280624847

Reorder the terms:
0.2 + n = 1.280624847

Solving
0.2 + n = 1.280624847

Solving for variable 'n'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + n = 1.280624847 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + n = 1.280624847 + -0.2
n = 1.280624847 + -0.2

Combine like terms: 1.280624847 + -0.2 = 1.080624847
n = 1.080624847

Simplifying
n = 1.080624847

Subproblem 2
n + 0.2 = -1.280624847

Simplifying
n + 0.2 = -1.280624847

Reorder the terms:
0.2 + n = -1.280624847

Solving
0.2 + n = -1.280624847

Solving for variable 'n'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + n = -1.280624847 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + n = -1.280624847 + -0.2
n = -1.280624847 + -0.2

Combine like terms: -1.280624847 + -0.2 = -1.480624847
n = -1.480624847

Simplifying
n = -1.480624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.080624847, -1.480624847}
Solution
n = {1.080624847, -1.480624847}