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

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

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

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

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

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

Reorder the terms:
1f + fn = 2f + 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
1f + fn = 2f + 0
1f + fn = 2f

Solving
1f + fn = 2f

Solving for variable 'f'.

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

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

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

Combine like terms: 2f + -2f = 0
-1f + fn = 0

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

Simplifying
-1 + n = 0

Solving
-1 + n = 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 + n = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -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}