8n(3n+5)=30

Solution for 8n(3n+5)=30 equation:

Simplifying
8n(3n + 5) = 30

Reorder the terms:
8n(5 + 3n) = 30
(5 * 8n + 3n * 8n) = 30
(40n + 24n2) = 30

Solving
40n + 24n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + 40n + 24n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 40n + 24n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 20n + 12n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 20n + 12n2)' equal to zero and attempt to solve:

Simplifying
-15 + 20n + 12n2 = 0

Solving
-15 + 20n + 12n2 = 0

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

Divide each side by '12'.
-1.25 + 1.666666667n + n2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 1.666666667n + 1.25 + n2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 1.666666667n + n2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 1.666666667n + n2 = 0 + 1.25
1.666666667n + n2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
1.666666667n + n2 = 1.25

The n term is 1.666666667n.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667n + 0.6944444447 + n2 = 1.25 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667n + n2 = 1.25 + 0.6944444447

Combine like terms: 1.25 + 0.6944444447 = 1.9444444447
0.6944444447 + 1.666666667n + n2 = 1.9444444447

Factor a perfect square on the left side:
(n + 0.8333333335)(n + 0.8333333335) = 1.9444444447

Calculate the square root of the right side: 1.394433378

Break this problem into two subproblems by setting 
(n + 0.8333333335) equal to 1.394433378 and -1.394433378.

Subproblem 1
n + 0.8333333335 = 1.394433378

Simplifying
n + 0.8333333335 = 1.394433378

Reorder the terms:
0.8333333335 + n = 1.394433378

Solving
0.8333333335 + n = 1.394433378

Solving for variable 'n'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + n = 1.394433378 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + n = 1.394433378 + -0.8333333335
n = 1.394433378 + -0.8333333335

Combine like terms: 1.394433378 + -0.8333333335 = 0.5611000445
n = 0.5611000445

Simplifying
n = 0.5611000445

Subproblem 2
n + 0.8333333335 = -1.394433378

Simplifying
n + 0.8333333335 = -1.394433378

Reorder the terms:
0.8333333335 + n = -1.394433378

Solving
0.8333333335 + n = -1.394433378

Solving for variable 'n'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + n = -1.394433378 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + n = -1.394433378 + -0.8333333335
n = -1.394433378 + -0.8333333335

Combine like terms: -1.394433378 + -0.8333333335 = -2.2277667115
n = -2.2277667115

Simplifying
n = -2.2277667115

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.5611000445, -2.2277667115}
Solution
n = {0.5611000445, -2.2277667115}