f(n)=4f(n-1)-f(n-2)-6f(n-3)

Solution for f(n)=4f(n-1)-f(n-2)-6f(n-3) equation:

Simplifying
f(n) = 4f(n + -1) + -1f(n + -2) + -6f(n + -3)

Multiply f * n
fn = 4f(n + -1) + -1f(n + -2) + -6f(n + -3)

Reorder the terms:
fn = 4f(-1 + n) + -1f(n + -2) + -6f(n + -3)
fn = (-1 * 4f + n * 4f) + -1f(n + -2) + -6f(n + -3)
fn = (-4f + 4fn) + -1f(n + -2) + -6f(n + -3)

Reorder the terms:
fn = -4f + 4fn + -1f(-2 + n) + -6f(n + -3)
fn = -4f + 4fn + (-2 * -1f + n * -1f) + -6f(n + -3)
fn = -4f + 4fn + (2f + -1fn) + -6f(n + -3)

Reorder the terms:
fn = -4f + 4fn + 2f + -1fn + -6f(-3 + n)
fn = -4f + 4fn + 2f + -1fn + (-3 * -6f + n * -6f)
fn = -4f + 4fn + 2f + -1fn + (18f + -6fn)

Reorder the terms:
fn = -4f + 2f + 18f + 4fn + -1fn + -6fn

Combine like terms: -4f + 2f = -2f
fn = -2f + 18f + 4fn + -1fn + -6fn

Combine like terms: -2f + 18f = 16f
fn = 16f + 4fn + -1fn + -6fn

Combine like terms: 4fn + -1fn = 3fn
fn = 16f + 3fn + -6fn

Combine like terms: 3fn + -6fn = -3fn
fn = 16f + -3fn

Solving
fn = 16f + -3fn

Solving for variable 'f'.

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

Add '-16f' to each side of the equation.
-16f + fn = 16f + -16f + -3fn

Combine like terms: 16f + -16f = 0
-16f + fn = 0 + -3fn
-16f + fn = -3fn

Add '3fn' to each side of the equation.
-16f + fn + 3fn = -3fn + 3fn

Combine like terms: fn + 3fn = 4fn
-16f + 4fn = -3fn + 3fn

Combine like terms: -3fn + 3fn = 0
-16f + 4fn = 0

Factor out the Greatest Common Factor (GCF), '4f'.
4f(-4 + n) = 0

Ignore the factor 4.
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 '(-4 + n)' equal to zero and attempt to solve:

Simplifying
-4 + n = 0

Solving
-4 + n = 0

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

Add '4' to each side of the equation.
-4 + 4 + n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + n = 0 + 4
n = 0 + 4

Combine like terms: 0 + 4 = 4
n = 4

Add '-1n' to each side of the equation.
n + -1n = 4 + -1n

Combine like terms: n + -1n = 0
0 = 4 + -1n

Simplifying
0 = 4 + -1n

The solution to this equation could not be determined.

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