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

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

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

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

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

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

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

Combine like terms: -1f + -2f = -3f
fn = -3f + fn + fn

Combine like terms: fn + fn = 2fn
fn = -3f + 2fn

Solving
fn = -3f + 2fn

Solving for variable 'f'.

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

Add '3f' to each side of the equation.
3f + fn = -3f + 3f + 2fn

Combine like terms: -3f + 3f = 0
3f + fn = 0 + 2fn
3f + fn = 2fn

Add '-2fn' to each side of the equation.
3f + fn + -2fn = 2fn + -2fn

Combine like terms: fn + -2fn = -1fn
3f + -1fn = 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
3f + -1fn = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(3 + -1n) = 0

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

Simplifying
f = 0

Solving
f = 0

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

Simplifying
f = 0
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Add 'n' to each side of the equation.
-1n + n = -3 + n

Combine like terms: -1n + n = 0
0 = -3 + n

Simplifying
0 = -3 + n

The solution to this equation could not be determined.

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