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

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

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

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

Reorder the terms:
fn = 2f(-2 + n) + f(n + -1)
fn = (-2 * 2f + n * 2f) + f(n + -1)
fn = (-4f + 2fn) + f(n + -1)

Reorder the terms:
fn = -4f + 2fn + f(-1 + n)
fn = -4f + 2fn + (-1 * f + n * f)
fn = -4f + 2fn + (-1f + fn)

Reorder the terms:
fn = -4f + -1f + 2fn + fn

Combine like terms: -4f + -1f = -5f
fn = -5f + 2fn + fn

Combine like terms: 2fn + fn = 3fn
fn = -5f + 3fn

Solving
fn = -5f + 3fn

Solving for variable 'f'.

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

Add '5f' to each side of the equation.
5f + fn = -5f + 5f + 3fn

Combine like terms: -5f + 5f = 0
5f + fn = 0 + 3fn
5f + fn = 3fn

Add '-3fn' to each side of the equation.
5f + fn + -3fn = 3fn + -3fn

Combine like terms: fn + -3fn = -2fn
5f + -2fn = 3fn + -3fn

Combine like terms: 3fn + -3fn = 0
5f + -2fn = 0

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

Simplifying
5 + -2n = 0

Solving
5 + -2n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Add '2n' to each side of the equation.
-2n + 2n = -5 + 2n

Combine like terms: -2n + 2n = 0
0 = -5 + 2n

Simplifying
0 = -5 + 2n

The solution to this equation could not be determined.

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