f(x)=f(-3)

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

Simplifying
f(x) = f(-3)

Multiply f * x
fx = f(-3)

Reorder the terms for easier multiplication:
fx = -3f

Solving
fx = -3f

Solving for variable 'f'.

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

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

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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

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

Simplifying
0 = -3 + -1x

The solution to this equation could not be determined.

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