5n(4n+8)=8

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

Simplifying
5n(4n + 8) = 8

Reorder the terms:
5n(8 + 4n) = 8
(8 * 5n + 4n * 5n) = 8
(40n + 20n2) = 8

Solving
40n + 20n2 = 8

Solving for variable 'n'.

Reorder the terms:
-8 + 40n + 20n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 40n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 10n + 5n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + 10n + 5n2)' equal to zero and attempt to solve:

Simplifying
-2 + 10n + 5n2 = 0

Solving
-2 + 10n + 5n2 = 0

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

Divide each side by '5'.
-0.4 + 2n + n2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2n + 0.4 + n2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2n + n2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2n + n2 = 0 + 0.4
2n + n2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2n + n2 = 0.4

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 0.4 + 1

Reorder the terms:
1 + 2n + n2 = 0.4 + 1

Combine like terms: 0.4 + 1 = 1.4
1 + 2n + n2 = 1.4

Factor a perfect square on the left side:
(n + 1)(n + 1) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(n + 1) equal to 1.183215957 and -1.183215957.

Subproblem 1
n + 1 = 1.183215957

Simplifying
n + 1 = 1.183215957

Reorder the terms:
1 + n = 1.183215957

Solving
1 + n = 1.183215957

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + n = 1.183215957 + -1
n = 1.183215957 + -1

Combine like terms: 1.183215957 + -1 = 0.183215957
n = 0.183215957

Simplifying
n = 0.183215957

Subproblem 2
n + 1 = -1.183215957

Simplifying
n + 1 = -1.183215957

Reorder the terms:
1 + n = -1.183215957

Solving
1 + n = -1.183215957

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + n = -1.183215957 + -1
n = -1.183215957 + -1

Combine like terms: -1.183215957 + -1 = -2.183215957
n = -2.183215957

Simplifying
n = -2.183215957

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.183215957, -2.183215957}
Solution
n = {0.183215957, -2.183215957}