n=(2n+8n^2+1)+(5n^2+5n+6)

Solution for n=(2n+8n^2+1)+(5n^2+5n+6) equation:

Simplifying
n = (2n + 8n2 + 1) + (5n2 + 5n + 6)

Reorder the terms:
n = (1 + 2n + 8n2) + (5n2 + 5n + 6)

Remove parenthesis around (1 + 2n + 8n2)
n = 1 + 2n + 8n2 + (5n2 + 5n + 6)

Reorder the terms:
n = 1 + 2n + 8n2 + (6 + 5n + 5n2)

Remove parenthesis around (6 + 5n + 5n2)
n = 1 + 2n + 8n2 + 6 + 5n + 5n2

Reorder the terms:
n = 1 + 6 + 2n + 5n + 8n2 + 5n2

Combine like terms: 1 + 6 = 7
n = 7 + 2n + 5n + 8n2 + 5n2

Combine like terms: 2n + 5n = 7n
n = 7 + 7n + 8n2 + 5n2

Combine like terms: 8n2 + 5n2 = 13n2
n = 7 + 7n + 13n2

Solving
n = 7 + 7n + 13n2

Solving for variable 'n'.

Reorder the terms:
-7 + n + -7n + -13n2 = 7 + 7n + 13n2 + -7 + -7n + -13n2

Combine like terms: n + -7n = -6n
-7 + -6n + -13n2 = 7 + 7n + 13n2 + -7 + -7n + -13n2

Reorder the terms:
-7 + -6n + -13n2 = 7 + -7 + 7n + -7n + 13n2 + -13n2

Combine like terms: 7 + -7 = 0
-7 + -6n + -13n2 = 0 + 7n + -7n + 13n2 + -13n2
-7 + -6n + -13n2 = 7n + -7n + 13n2 + -13n2

Combine like terms: 7n + -7n = 0
-7 + -6n + -13n2 = 0 + 13n2 + -13n2
-7 + -6n + -13n2 = 13n2 + -13n2

Combine like terms: 13n2 + -13n2 = 0
-7 + -6n + -13n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 6n + 13n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 6n + 13n2)' equal to zero and attempt to solve:

Simplifying
7 + 6n + 13n2 = 0

Solving
7 + 6n + 13n2 = 0

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

Divide each side by '13'.
0.5384615385 + 0.4615384615n + n2 = 0

Move the constant term to the right:

Add '-0.5384615385' to each side of the equation.
0.5384615385 + 0.4615384615n + -0.5384615385 + n2 = 0 + -0.5384615385

Reorder the terms:
0.5384615385 + -0.5384615385 + 0.4615384615n + n2 = 0 + -0.5384615385

Combine like terms: 0.5384615385 + -0.5384615385 = 0.0000000000
0.0000000000 + 0.4615384615n + n2 = 0 + -0.5384615385
0.4615384615n + n2 = 0 + -0.5384615385

Combine like terms: 0 + -0.5384615385 = -0.5384615385
0.4615384615n + n2 = -0.5384615385

The n term is 0.4615384615n.  Take half its coefficient (0.2307692308).
Square it (0.05325443788) and add it to both sides.

Add '0.05325443788' to each side of the equation.
0.4615384615n + 0.05325443788 + n2 = -0.5384615385 + 0.05325443788

Reorder the terms:
0.05325443788 + 0.4615384615n + n2 = -0.5384615385 + 0.05325443788

Combine like terms: -0.5384615385 + 0.05325443788 = -0.48520710062
0.05325443788 + 0.4615384615n + n2 = -0.48520710062

Factor a perfect square on the left side:
(n + 0.2307692308)(n + 0.2307692308) = -0.48520710062

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.