F(x)=f(3+x)-f(3)

Solution for F(x)=f(3+x)-f(3) equation:

Simplifying
F(x) = f(3 + x) + -1f(3)

Multiply F * x
xF = f(3 + x) + -1f(3)
xF = (3 * f + x * f) + -1f(3)
xF = (3f + fx) + -1f(3)

Reorder the terms for easier multiplication:
xF = 3f + fx + -1 * 3f

Multiply -1 * 3
xF = 3f + fx + -3f

Reorder the terms:
xF = 3f + -3f + fx

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

Solving
xF = fx

Solving for variable 'x'.

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

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

Combine like terms: fx + -1fx = 0
-1fx + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1f + F) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1f + F)' equal to zero and attempt to solve:

Simplifying
-1f + F = 0

Reorder the terms:
F + -1f = 0

Solving
F + -1f = 0

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

Add '-1F' to each side of the equation.
F + -1F + -1f = 0 + -1F

Combine like terms: F + -1F = 0
0 + -1f = 0 + -1F
-1f = 0 + -1F
Remove the zero:
-1f = -1F

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

Combine like terms: -1f + f = 0
0 = -1F + f

Simplifying
0 = -1F + f

The solution to this equation could not be determined.

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