f(n)=6f(n-1)-9f(n-2)

Solution for f(n)=6f(n-1)-9f(n-2) equation:

Simplifying
f(n) = 6f(n + -1) + -9f(n + -2)

Multiply f * n
fn = 6f(n + -1) + -9f(n + -2)

Reorder the terms:
fn = 6f(-1 + n) + -9f(n + -2)
fn = (-1 * 6f + n * 6f) + -9f(n + -2)
fn = (-6f + 6fn) + -9f(n + -2)

Reorder the terms:
fn = -6f + 6fn + -9f(-2 + n)
fn = -6f + 6fn + (-2 * -9f + n * -9f)
fn = -6f + 6fn + (18f + -9fn)

Reorder the terms:
fn = -6f + 18f + 6fn + -9fn

Combine like terms: -6f + 18f = 12f
fn = 12f + 6fn + -9fn

Combine like terms: 6fn + -9fn = -3fn
fn = 12f + -3fn

Solving
fn = 12f + -3fn

Solving for variable 'f'.

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

Add '-12f' to each side of the equation.
-12f + fn = 12f + -12f + -3fn

Combine like terms: 12f + -12f = 0
-12f + fn = 0 + -3fn
-12f + fn = -3fn

Add '3fn' to each side of the equation.
-12f + fn + 3fn = -3fn + 3fn

Combine like terms: fn + 3fn = 4fn
-12f + 4fn = -3fn + 3fn

Combine like terms: -3fn + 3fn = 0
-12f + 4fn = 0

Factor out the Greatest Common Factor (GCF), '4f'.
4f(-3 + 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 '(-3 + n)' equal to zero and attempt to solve:

Simplifying
-3 + n = 0

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

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

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

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

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

Simplifying
0 = 3 + -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}