(8n^3+9n^2-6n)+(-5n-4n^2+3n^3)=

Solution for (8n^3+9n^2-6n)+(-5n-4n^2+3n^3)= equation:

Simplifying
(8n3 + 9n2 + -6n) + (-5n + -4n2 + 3n3) = 0

Reorder the terms:
(-6n + 9n2 + 8n3) + (-5n + -4n2 + 3n3) = 0

Remove parenthesis around (-6n + 9n2 + 8n3)
-6n + 9n2 + 8n3 + (-5n + -4n2 + 3n3) = 0

Remove parenthesis around (-5n + -4n2 + 3n3)
-6n + 9n2 + 8n3 + -5n + -4n2 + 3n3 = 0

Reorder the terms:
-6n + -5n + 9n2 + -4n2 + 8n3 + 3n3 = 0

Combine like terms: -6n + -5n = -11n
-11n + 9n2 + -4n2 + 8n3 + 3n3 = 0

Combine like terms: 9n2 + -4n2 = 5n2
-11n + 5n2 + 8n3 + 3n3 = 0

Combine like terms: 8n3 + 3n3 = 11n3
-11n + 5n2 + 11n3 = 0

Solving
-11n + 5n2 + 11n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-11 + 5n + 11n2) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-11 + 5n + 11n2)' equal to zero and attempt to solve:

Simplifying
-11 + 5n + 11n2 = 0

Solving
-11 + 5n + 11n2 = 0

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

Divide each side by '11'.
-1 + 0.4545454545n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.4545454545n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.4545454545n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.4545454545n + n2 = 0 + 1
0.4545454545n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.4545454545n + n2 = 1

The n term is 0.4545454545n.  Take half its coefficient (0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
0.4545454545n + 0.05165289257 + n2 = 1 + 0.05165289257

Reorder the terms:
0.05165289257 + 0.4545454545n + n2 = 1 + 0.05165289257

Combine like terms: 1 + 0.05165289257 = 1.05165289257
0.05165289257 + 0.4545454545n + n2 = 1.05165289257

Factor a perfect square on the left side:
(n + 0.2272727273)(n + 0.2272727273) = 1.05165289257

Calculate the square root of the right side: 1.025501288

Break this problem into two subproblems by setting 
(n + 0.2272727273) equal to 1.025501288 and -1.025501288.

Subproblem 1
n + 0.2272727273 = 1.025501288

Simplifying
n + 0.2272727273 = 1.025501288

Reorder the terms:
0.2272727273 + n = 1.025501288

Solving
0.2272727273 + n = 1.025501288

Solving for variable 'n'.

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

Add '-0.2272727273' to each side of the equation.
0.2272727273 + -0.2272727273 + n = 1.025501288 + -0.2272727273

Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000
0.0000000000 + n = 1.025501288 + -0.2272727273
n = 1.025501288 + -0.2272727273

Combine like terms: 1.025501288 + -0.2272727273 = 0.7982285607
n = 0.7982285607

Simplifying
n = 0.7982285607

Subproblem 2
n + 0.2272727273 = -1.025501288

Simplifying
n + 0.2272727273 = -1.025501288

Reorder the terms:
0.2272727273 + n = -1.025501288

Solving
0.2272727273 + n = -1.025501288

Solving for variable 'n'.

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

Add '-0.2272727273' to each side of the equation.
0.2272727273 + -0.2272727273 + n = -1.025501288 + -0.2272727273

Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000
0.0000000000 + n = -1.025501288 + -0.2272727273
n = -1.025501288 + -0.2272727273

Combine like terms: -1.025501288 + -0.2272727273 = -1.2527740153
n = -1.2527740153

Simplifying
n = -1.2527740153

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.7982285607, -1.2527740153}
Solution
n = {0, 0.7982285607, -1.2527740153}