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

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

Simplifying
f(-3) = f(x + y)

Reorder the terms for easier multiplication:
-3f = f(x + y)
-3f = (x * f + y * f)
-3f = (fx + fy)

Solving
-3f = fx + fy

Solving for variable 'f'.

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

Add '-1fx' to each side of the equation.
-3f + -1fx = fx + -1fx + fy

Combine like terms: fx + -1fx = 0
-3f + -1fx = 0 + fy
-3f + -1fx = fy

Add '-1fy' to each side of the equation.
-3f + -1fx + -1fy = fy + -1fy

Combine like terms: fy + -1fy = 0
-3f + -1fx + -1fy = 0

Factor out the Greatest Common Factor (GCF), '-1f'.
-1f(3 + x + y) = 0

Ignore the factor -1.
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 '(3 + x + y)' equal to zero and attempt to solve:

Simplifying
3 + x + y = 0

Solving
3 + x + y = 0

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

Add '-3' to each side of the equation.
3 + x + -3 + y = 0 + -3

Reorder the terms:
3 + -3 + x + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x + y = 0 + -3
x + y = 0 + -3

Combine like terms: 0 + -3 = -3
x + y = -3

Add '-1x' to each side of the equation.
x + -1x + y = -3 + -1x

Combine like terms: x + -1x = 0
0 + y = -3 + -1x
y = -3 + -1x

Add '-1y' to each side of the equation.
y + -1y = -3 + -1x + -1y

Combine like terms: y + -1y = 0
0 = -3 + -1x + -1y

Simplifying
0 = -3 + -1x + -1y

The solution to this equation could not be determined.

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