f(2n)=f(n)+f(n+1)+n

Solution for f(2n)=f(n)+f(n+1)+n equation:

Simplifying
f(2n) = f(n) + f(n + 1) + n

Remove parenthesis around (2n)
f * 2n = f(n) + f(n + 1) + n

Reorder the terms for easier multiplication:
2f * n = f(n) + f(n + 1) + n

Multiply f * n
2fn = f(n) + f(n + 1) + n

Multiply f * n
2fn = fn + f(n + 1) + n

Reorder the terms:
2fn = fn + f(1 + n) + n
2fn = fn + (1 * f + n * f) + n
2fn = fn + (1f + fn) + n

Reorder the terms:
2fn = 1f + fn + fn + n

Combine like terms: fn + fn = 2fn
2fn = 1f + 2fn + n

Add '-2fn' to each side of the equation.
2fn + -2fn = 1f + 2fn + -2fn + n

Combine like terms: 2fn + -2fn = 0
0 = 1f + 2fn + -2fn + n

Combine like terms: 2fn + -2fn = 0
0 = 1f + 0 + n
0 = 1f + n

Solving
0 = 1f + n

Solving for variable 'f'.

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

Add '-1f' to each side of the equation.
0 + -1f = 1f + -1f + n
Remove the zero:
-1f = 1f + -1f + n

Combine like terms: 1f + -1f = 0
-1f = 0 + n
-1f = n

Divide each side by '-1'.
f = -1n

Simplifying
f = -1n