8n(5n+4)=2

Solution for 8n(5n+4)=2 equation:

Simplifying
8n(5n + 4) = 2

Reorder the terms:
8n(4 + 5n) = 2
(4 * 8n + 5n * 8n) = 2
(32n + 40n2) = 2

Solving
32n + 40n2 = 2

Solving for variable 'n'.

Reorder the terms:
-2 + 32n + 40n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 32n + 40n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 16n + 20n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 16n + 20n2)' equal to zero and attempt to solve:

Simplifying
-1 + 16n + 20n2 = 0

Solving
-1 + 16n + 20n2 = 0

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

Divide each side by '20'.
-0.05 + 0.8n + n2 = 0.0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + 0.8n + 0.05 + n2 = 0.0 + 0.05

Reorder the terms:
-0.05 + 0.05 + 0.8n + n2 = 0.0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + 0.8n + n2 = 0.0 + 0.05
0.8n + n2 = 0.0 + 0.05

Combine like terms: 0.0 + 0.05 = 0.05
0.8n + n2 = 0.05

The n term is 0.8n.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8n + 0.16 + n2 = 0.05 + 0.16

Reorder the terms:
0.16 + 0.8n + n2 = 0.05 + 0.16

Combine like terms: 0.05 + 0.16 = 0.21
0.16 + 0.8n + n2 = 0.21

Factor a perfect square on the left side:
(n + 0.4)(n + 0.4) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(n + 0.4) equal to 0.458257569 and -0.458257569.

Subproblem 1
n + 0.4 = 0.458257569

Simplifying
n + 0.4 = 0.458257569

Reorder the terms:
0.4 + n = 0.458257569

Solving
0.4 + n = 0.458257569

Solving for variable 'n'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + n = 0.458257569 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + n = 0.458257569 + -0.4
n = 0.458257569 + -0.4

Combine like terms: 0.458257569 + -0.4 = 0.058257569
n = 0.058257569

Simplifying
n = 0.058257569

Subproblem 2
n + 0.4 = -0.458257569

Simplifying
n + 0.4 = -0.458257569

Reorder the terms:
0.4 + n = -0.458257569

Solving
0.4 + n = -0.458257569

Solving for variable 'n'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + n = -0.458257569 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + n = -0.458257569 + -0.4
n = -0.458257569 + -0.4

Combine like terms: -0.458257569 + -0.4 = -0.858257569
n = -0.858257569

Simplifying
n = -0.858257569

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.058257569, -0.858257569}
Solution
n = {0.058257569, -0.858257569}