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

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

Simplifying
(2n + -8n2) + (5n3 + 4n2) = 0

Remove parenthesis around (2n + -8n2)
2n + -8n2 + (5n3 + 4n2) = 0

Reorder the terms:
2n + -8n2 + (4n2 + 5n3) = 0

Remove parenthesis around (4n2 + 5n3)
2n + -8n2 + 4n2 + 5n3 = 0

Combine like terms: -8n2 + 4n2 = -4n2
2n + -4n2 + 5n3 = 0

Solving
2n + -4n2 + 5n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(2 + -4n + 5n2) = 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 '(2 + -4n + 5n2)' equal to zero and attempt to solve:

Simplifying
2 + -4n + 5n2 = 0

Solving
2 + -4n + 5n2 = 0

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

Divide each side by '5'.
0.4 + -0.8n + n2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -0.8n + -0.4 + n2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -0.8n + n2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -0.8n + n2 = 0 + -0.4
-0.8n + n2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-0.8n + n2 = -0.4

The n term is -0.8n.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8n + 0.16 + n2 = -0.4 + 0.16

Reorder the terms:
0.16 + -0.8n + n2 = -0.4 + 0.16

Combine like terms: -0.4 + 0.16 = -0.24
0.16 + -0.8n + n2 = -0.24

Factor a perfect square on the left side:
(n + -0.4)(n + -0.4) = -0.24

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.
Solution
n = {0}