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

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

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

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

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

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

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

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

Combine like terms: 2fn + fn = 3fn
fn = -4f + 3fn

Solving
fn = -4f + 3fn

Solving for variable 'f'.

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

Add '4f' to each side of the equation.
4f + fn = -4f + 4f + 3fn

Combine like terms: -4f + 4f = 0
4f + fn = 0 + 3fn
4f + fn = 3fn

Add '-3fn' to each side of the equation.
4f + fn + -3fn = 3fn + -3fn

Combine like terms: fn + -3fn = -2fn
4f + -2fn = 3fn + -3fn

Combine like terms: 3fn + -3fn = 0
4f + -2fn = 0

Factor out the Greatest Common Factor (GCF), '2f'.
2f(2 + -1n) = 0

Ignore the factor 2.
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 '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

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

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

Simplifying
0 = -2 + 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}