f(x)=f(x-4)+f(2x-1)

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


Simplifying
f(x) = f(x + -4) + f(2x + -1)

Multiply f * x
fx = f(x + -4) + f(2x + -1)

Reorder the terms:
fx = f(-4 + x) + f(2x + -1)
fx = (-4 * f + x * f) + f(2x + -1)
fx = (-4f + fx) + f(2x + -1)

Reorder the terms:
fx = -4f + fx + f(-1 + 2x)
fx = -4f + fx + (-1 * f + 2x * f)
fx = -4f + fx + (-1f + 2fx)

Reorder the terms:
fx = -4f + -1f + fx + 2fx

Combine like terms: -4f + -1f = -5f
fx = -5f + fx + 2fx

Combine like terms: fx + 2fx = 3fx
fx = -5f + 3fx

Solving
fx = -5f + 3fx

Solving for variable 'f'.

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

Add '5f' to each side of the equation.
5f + fx = -5f + 5f + 3fx

Combine like terms: -5f + 5f = 0
5f + fx = 0 + 3fx
5f + fx = 3fx

Add '-3fx' to each side of the equation.
5f + fx + -3fx = 3fx + -3fx

Combine like terms: fx + -3fx = -2fx
5f + -2fx = 3fx + -3fx

Combine like terms: 3fx + -3fx = 0
5f + -2fx = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Add '2x' to each side of the equation.
-2x + 2x = -5 + 2x

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 2x

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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