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

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

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

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

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

Multiply f * n
2f + fn = 1f + fn + 4fn

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

Solving
2f + fn = 1f + 5fn

Solving for variable 'f'.

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

Add '-1f' to each side of the equation.
2f + -1f + fn = 1f + -1f + 5fn

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

Combine like terms: 1f + -1f = 0
1f + fn = 0 + 5fn
1f + fn = 5fn

Add '-5fn' to each side of the equation.
1f + fn + -5fn = 5fn + -5fn

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

Combine like terms: 5fn + -5fn = 0
1f + -4fn = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(1 + -4n) = 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 '(1 + -4n)' equal to zero and attempt to solve:

Simplifying
1 + -4n = 0

Solving
1 + -4n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4n = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 4n

The solution to this equation could not be determined.

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