n+n+1+n+2+n+3+n+4=0

Solution for n+n+1+n+2+n+3+n+4=0 equation:

Simplifying
n + n + 1 + n + 2 + n + 3 + n + 4 = 0

Reorder the terms:
1 + 2 + 3 + 4 + n + n + n + n + n = 0

Combine like terms: 1 + 2 = 3
3 + 3 + 4 + n + n + n + n + n = 0

Combine like terms: 3 + 3 = 6
6 + 4 + n + n + n + n + n = 0

Combine like terms: 6 + 4 = 10
10 + n + n + n + n + n = 0

Combine like terms: n + n = 2n
10 + 2n + n + n + n = 0

Combine like terms: 2n + n = 3n
10 + 3n + n + n = 0

Combine like terms: 3n + n = 4n
10 + 4n + n = 0

Combine like terms: 4n + n = 5n
10 + 5n = 0

Solving
10 + 5n = 0

Solving for variable 'n'.

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

Add '-10' to each side of the equation.
10 + -10 + 5n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 5n = 0 + -10
5n = 0 + -10

Combine like terms: 0 + -10 = -10
5n = -10

Divide each side by '5'.
n = -2

Simplifying
n = -2