f(x+3y)=2f(x)-3f(y)

Solution for f(x+3y)=2f(x)-3f(y) equation:

Simplifying
f(x + 3y) = 2f(x) + -3f(y)
(x * f + 3y * f) = 2f(x) + -3f(y)
(fx + 3fy) = 2f(x) + -3f(y)

Multiply f * x
fx + 3fy = 2fx + -3f(y)

Multiply f * y
fx + 3fy = 2fx + -3fy

Solving
fx + 3fy = 2fx + -3fy

Solving for variable 'f'.

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

Add '-2fx' to each side of the equation.
fx + -2fx + 3fy = 2fx + -2fx + -3fy

Combine like terms: fx + -2fx = -1fx
-1fx + 3fy = 2fx + -2fx + -3fy

Combine like terms: 2fx + -2fx = 0
-1fx + 3fy = 0 + -3fy
-1fx + 3fy = -3fy

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

Combine like terms: 3fy + 3fy = 6fy
-1fx + 6fy = -3fy + 3fy

Combine like terms: -3fy + 3fy = 0
-1fx + 6fy = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(-1x + 6y) = 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 '(-1x + 6y)' equal to zero and attempt to solve:

Simplifying
-1x + 6y = 0

Solving
-1x + 6y = 0

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

Add 'x' to each side of the equation.
-1x + x + 6y = 0 + x

Combine like terms: -1x + x = 0
0 + 6y = 0 + x
6y = 0 + x
Remove the zero:
6y = x

Add '-6y' to each side of the equation.
6y + -6y = x + -6y

Combine like terms: 6y + -6y = 0
0 = x + -6y

Simplifying
0 = x + -6y

The solution to this equation could not be determined.

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