f(x+y)=f(x)+f(y)+xy

Solution for f(x+y)=f(x)+f(y)+xy equation:

Simplifying
f(x + y) = f(x) + f(y) + xy
(x * f + y * f) = f(x) + f(y) + xy
(fx + fy) = f(x) + f(y) + xy

Multiply f * x
fx + fy = fx + f(y) + xy

Multiply f * y
fx + fy = fx + fy + xy

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

Combine like terms: fx + -1fx = 0
0 + fy = fx + fy + -1fx + xy
fy = fx + fy + -1fx + xy

Reorder the terms:
fy = fx + -1fx + fy + xy

Combine like terms: fx + -1fx = 0
fy = 0 + fy + xy
fy = fy + xy

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

Combine like terms: fy + -1fy = 0
0 = fy + -1fy + xy

Combine like terms: fy + -1fy = 0
0 = 0 + xy
0 = xy

Solving
0 = xy

Solving for variable 'x'.

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

Add '-1xy' to each side of the equation.
0 + -1xy = xy + -1xy
Remove the zero:
-1xy = xy + -1xy

Combine like terms: xy + -1xy = 0
-1xy = 0

Divide each side by '-1'.
xy = 0

Simplifying
xy = 0

The solution to this equation could not be determined.