f(n)=4f(n-1)+f(n-2)

Solution for f(n)=4f(n-1)+f(n-2) equation:

Simplifying
f(n) = 4f(n + -1) + f(n + -2)

Multiply f * n
fn = 4f(n + -1) + f(n + -2)

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

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

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

Combine like terms: -4f + -2f = -6f
fn = -6f + 4fn + fn

Combine like terms: 4fn + fn = 5fn
fn = -6f + 5fn

Solving
fn = -6f + 5fn

Solving for variable 'f'.

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

Add '6f' to each side of the equation.
6f + fn = -6f + 6f + 5fn

Combine like terms: -6f + 6f = 0
6f + fn = 0 + 5fn
6f + fn = 5fn

Add '-5fn' to each side of the equation.
6f + fn + -5fn = 5fn + -5fn

Combine like terms: fn + -5fn = -4fn
6f + -4fn = 5fn + -5fn

Combine like terms: 5fn + -5fn = 0
6f + -4fn = 0

Factor out the Greatest Common Factor (GCF), '2f'.
2f(3 + -2n) = 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 '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

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

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

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

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

Simplifying
0 = -3 + 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}