-n(-n^3+8)+(-n)(7n^3+1)=

Solution for -n(-n^3+8)+(-n)(7n^3+1)= equation:

Simplifying
-1n(-1n3 + 8) + (-1n)(7n3 + 1) = 0

Reorder the terms:
-1n(8 + -1n3) + (-1n)(7n3 + 1) = 0
(8 * -1n + -1n3 * -1n) + (-1n)(7n3 + 1) = 0
(-8n + 1n4) + (-1n)(7n3 + 1) = 0

Remove parenthesis around (-1n)
-8n + 1n4 + -1n(7n3 + 1) = 0

Reorder the terms:
-8n + 1n4 + -1n(1 + 7n3) = 0
-8n + 1n4 + (1 * -1n + 7n3 * -1n) = 0
-8n + 1n4 + (-1n + -7n4) = 0

Reorder the terms:
-8n + -1n + 1n4 + -7n4 = 0

Combine like terms: -8n + -1n = -9n
-9n + 1n4 + -7n4 = 0

Combine like terms: 1n4 + -7n4 = -6n4
-9n + -6n4 = 0

Solving
-9n + -6n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-3n'.
-3n(3 + 2n3) = 0

Ignore the factor -3.
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 '(3 + 2n3)' equal to zero and attempt to solve:

Simplifying
3 + 2n3 = 0

Solving
3 + 2n3 = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2n3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n3 = 0 + -3
2n3 = 0 + -3

Combine like terms: 0 + -3 = -3
2n3 = -3

Divide each side by '2'.
n3 = -1.5

Simplifying
n3 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}