f(x+f(x))=4f(x)

Solution for f(x+f(x))=4f(x) equation:

Simplifying
f(x + f(x)) = 4f(x)

Multiply f * x
f(x + fx) = 4f(x)

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

Reorder the terms:
(fx + f2x) = 4f(x)
(fx + f2x) = 4f(x)

Multiply f * x
fx + f2x = 4fx

Solving
fx + f2x = 4fx

Solving for variable 'f'.

Reorder the terms:
fx + -4fx + f2x = 4fx + -4fx

Combine like terms: fx + -4fx = -3fx
-3fx + f2x = 4fx + -4fx

Combine like terms: 4fx + -4fx = 0
-3fx + f2x = 0

Factor out the Greatest Common Factor (GCF), 'fx'.
fx(-3 + f) = 0

Subproblem 1
Set the factor 'fx' equal to zero and attempt to solve:

Simplifying
fx = 0

Solving
fx = 0

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

Simplifying
fx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + f)' equal to zero and attempt to solve:

Simplifying
-3 + f = 0

Solving
-3 + f = 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 + f = 0 + 3

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

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

Simplifying
f = 3
Solution
f = {3}