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

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


Simplifying
F(x + y + -1xy) = f(x) + f(y) + -1f(x) * f(y)

Reorder the terms:
F(x + -1xy + y) = f(x) + f(y) + -1f(x) * f(y)
(x * F + -1xy * F + y * F) = f(x) + f(y) + -1f(x) * f(y)
(xF + -1xyF + yF) = f(x) + f(y) + -1f(x) * f(y)

Multiply f * x
xF + -1xyF + yF = fx + f(y) + -1f(x) * f(y)

Multiply f * y
xF + -1xyF + yF = fx + fy + -1f(x) * f(y)

Multiply f * x
xF + -1xyF + yF = fx + fy + -1fx * f * y

Multiply fx * f
xF + -1xyF + yF = fx + fy + -1f2x * y

Multiply f2x * y
xF + -1xyF + yF = fx + fy + -1f2xy

Solving
xF + -1xyF + yF = fx + fy + -1f2xy

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.
xF + -1xyF + -1fx + yF = fx + fy + -1fx + -1f2xy

Reorder the terms:
-1fx + xF + -1xyF + yF = fx + fy + -1fx + -1f2xy

Reorder the terms:
-1fx + xF + -1xyF + yF = fx + -1fx + fy + -1f2xy

Combine like terms: fx + -1fx = 0
-1fx + xF + -1xyF + yF = 0 + fy + -1f2xy
-1fx + xF + -1xyF + yF = fy + -1f2xy

Add 'f2xy' to each side of the equation.
-1fx + xF + -1xyF + f2xy + yF = fy + -1f2xy + f2xy

Reorder the terms:
-1fx + f2xy + xF + -1xyF + yF = fy + -1f2xy + f2xy

Combine like terms: -1f2xy + f2xy = 0
-1fx + f2xy + xF + -1xyF + yF = fy + 0
-1fx + f2xy + xF + -1xyF + yF = fy

Add '-1yF' to each side of the equation.
-1fx + f2xy + xF + -1xyF + yF + -1yF = fy + -1yF

Combine like terms: yF + -1yF = 0
-1fx + f2xy + xF + -1xyF + 0 = fy + -1yF
-1fx + f2xy + xF + -1xyF = fy + -1yF

Reorder the terms:
-1fx + -1fy + f2xy + xF + -1xyF + yF = fy + -1yF + -1fy + yF

Reorder the terms:
-1fx + -1fy + f2xy + xF + -1xyF + yF = fy + -1fy + -1yF + yF

Combine like terms: fy + -1fy = 0
-1fx + -1fy + f2xy + xF + -1xyF + yF = 0 + -1yF + yF
-1fx + -1fy + f2xy + xF + -1xyF + yF = -1yF + yF

Combine like terms: -1yF + yF = 0
-1fx + -1fy + f2xy + xF + -1xyF + yF = 0

The solution to this equation could not be determined.

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