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

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


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

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

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

Solving
fn = 2f + -2fn

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.
-2f + fn = 2f + -2f + -2fn

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

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

Combine like terms: fn + 2fn = 3fn
-2f + 3fn = -2fn + 2fn

Combine like terms: -2fn + 2fn = 0
-2f + 3fn = 0

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

Simplifying
-2 + 3n = 0

Solving
-2 + 3n = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3n = 0 + 2

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

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

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

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

Simplifying
0 = 2 + -3n

The solution to this equation could not be determined.

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

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