8n(2n+5)=37

Solution for 8n(2n+5)=37 equation:

Simplifying
8n(2n + 5) = 37

Reorder the terms:
8n(5 + 2n) = 37
(5 * 8n + 2n * 8n) = 37
(40n + 16n2) = 37

Solving
40n + 16n2 = 37

Solving for variable 'n'.

Reorder the terms:
-37 + 40n + 16n2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 40n + 16n2 = 0

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

Divide each side by '16'.
-2.3125 + 2.5n + n2 = 0

Move the constant term to the right:

Add '2.3125' to each side of the equation.
-2.3125 + 2.5n + 2.3125 + n2 = 0 + 2.3125

Reorder the terms:
-2.3125 + 2.3125 + 2.5n + n2 = 0 + 2.3125

Combine like terms: -2.3125 + 2.3125 = 0.0000
0.0000 + 2.5n + n2 = 0 + 2.3125
2.5n + n2 = 0 + 2.3125

Combine like terms: 0 + 2.3125 = 2.3125
2.5n + n2 = 2.3125

The n term is 2.5n.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5n + 1.5625 + n2 = 2.3125 + 1.5625

Reorder the terms:
1.5625 + 2.5n + n2 = 2.3125 + 1.5625

Combine like terms: 2.3125 + 1.5625 = 3.875
1.5625 + 2.5n + n2 = 3.875

Factor a perfect square on the left side:
(n + 1.25)(n + 1.25) = 3.875

Calculate the square root of the right side: 1.968501969

Break this problem into two subproblems by setting 
(n + 1.25) equal to 1.968501969 and -1.968501969.

Subproblem 1
n + 1.25 = 1.968501969

Simplifying
n + 1.25 = 1.968501969

Reorder the terms:
1.25 + n = 1.968501969

Solving
1.25 + n = 1.968501969

Solving for variable 'n'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + n = 1.968501969 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + n = 1.968501969 + -1.25
n = 1.968501969 + -1.25

Combine like terms: 1.968501969 + -1.25 = 0.718501969
n = 0.718501969

Simplifying
n = 0.718501969

Subproblem 2
n + 1.25 = -1.968501969

Simplifying
n + 1.25 = -1.968501969

Reorder the terms:
1.25 + n = -1.968501969

Solving
1.25 + n = -1.968501969

Solving for variable 'n'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + n = -1.968501969 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + n = -1.968501969 + -1.25
n = -1.968501969 + -1.25

Combine like terms: -1.968501969 + -1.25 = -3.218501969
n = -3.218501969

Simplifying
n = -3.218501969

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.718501969, -3.218501969}