3+16n=-15n^2

Solution for 3+16n=-15n^2 equation:

Simplifying
3 + 16n = -15n2

Solving
3 + 16n = -15n2

Solving for variable 'n'.

Combine like terms: -15n2 + 15n2 = 0
3 + 16n + 15n2 = 0

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

Divide each side by '15'.
0.2 + 1.066666667n + n2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.066666667n + -0.2 + n2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.066666667n + n2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.066666667n + n2 = 0 + -0.2
1.066666667n + n2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.066666667n + n2 = -0.2

The n term is 1.066666667n.  Take half its coefficient (0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
1.066666667n + 0.2844444446 + n2 = -0.2 + 0.2844444446

Reorder the terms:
0.2844444446 + 1.066666667n + n2 = -0.2 + 0.2844444446

Combine like terms: -0.2 + 0.2844444446 = 0.0844444446
0.2844444446 + 1.066666667n + n2 = 0.0844444446

Factor a perfect square on the left side:
(n + 0.5333333335)(n + 0.5333333335) = 0.0844444446

Calculate the square root of the right side: 0.290593263

Break this problem into two subproblems by setting 
(n + 0.5333333335) equal to 0.290593263 and -0.290593263.

Subproblem 1
n + 0.5333333335 = 0.290593263

Simplifying
n + 0.5333333335 = 0.290593263

Reorder the terms:
0.5333333335 + n = 0.290593263

Solving
0.5333333335 + n = 0.290593263

Solving for variable 'n'.

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

Add '-0.5333333335' to each side of the equation.
0.5333333335 + -0.5333333335 + n = 0.290593263 + -0.5333333335

Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000
0.0000000000 + n = 0.290593263 + -0.5333333335
n = 0.290593263 + -0.5333333335

Combine like terms: 0.290593263 + -0.5333333335 = -0.2427400705
n = -0.2427400705

Simplifying
n = -0.2427400705

Subproblem 2
n + 0.5333333335 = -0.290593263

Simplifying
n + 0.5333333335 = -0.290593263

Reorder the terms:
0.5333333335 + n = -0.290593263

Solving
0.5333333335 + n = -0.290593263

Solving for variable 'n'.

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

Add '-0.5333333335' to each side of the equation.
0.5333333335 + -0.5333333335 + n = -0.290593263 + -0.5333333335

Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000
0.0000000000 + n = -0.290593263 + -0.5333333335
n = -0.290593263 + -0.5333333335

Combine like terms: -0.290593263 + -0.5333333335 = -0.8239265965
n = -0.8239265965

Simplifying
n = -0.8239265965

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.2427400705, -0.8239265965}