F(x)+f(2x+y)+5XY=f(3x+y)+2x-1

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Solution for F(x)+f(2x+y)+5XY=f(3x+y)+2x-1 equation: 


Simplifying
F(x) + f(2x + y) + 5XY = f(3x + y) + 2x + -1

Multiply F * x
xF + f(2x + y) + 5XY = f(3x + y) + 2x + -1
xF + (2x * f + y * f) + 5XY = f(3x + y) + 2x + -1
xF + (2fx + fy) + 5XY = f(3x + y) + 2x + -1

Reorder the terms:
5XY + 2fx + fy + xF = f(3x + y) + 2x + -1
5XY + 2fx + fy + xF = (3x * f + y * f) + 2x + -1
5XY + 2fx + fy + xF = (3fx + fy) + 2x + -1

Reorder the terms:
5XY + 2fx + fy + xF = -1 + 3fx + fy + 2x

Add '-1fy' to each side of the equation.
5XY + 2fx + fy + -1fy + xF = -1 + 3fx + fy + -1fy + 2x

Combine like terms: fy + -1fy = 0
5XY + 2fx + 0 + xF = -1 + 3fx + fy + -1fy + 2x
5XY + 2fx + xF = -1 + 3fx + fy + -1fy + 2x

Combine like terms: fy + -1fy = 0
5XY + 2fx + xF = -1 + 3fx + 0 + 2x
5XY + 2fx + xF = -1 + 3fx + 2x

Solving
5XY + 2fx + xF = -1 + 3fx + 2x

Solving for variable 'X'.

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

Add '-2fx' to each side of the equation.
5XY + 2fx + -2fx + xF = -1 + 3fx + -2fx + 2x

Combine like terms: 2fx + -2fx = 0
5XY + 0 + xF = -1 + 3fx + -2fx + 2x
5XY + xF = -1 + 3fx + -2fx + 2x

Combine like terms: 3fx + -2fx = 1fx
5XY + xF = -1 + 1fx + 2x

Add '-1xF' to each side of the equation.
5XY + xF + -1xF = -1 + 1fx + 2x + -1xF

Combine like terms: xF + -1xF = 0
5XY + 0 = -1 + 1fx + 2x + -1xF
5XY = -1 + 1fx + 2x + -1xF

Divide each side by '5Y'.
X = -0.2Y-1 + 0.2fxY-1 + 0.4xY-1 + -0.2xFY-1

Simplifying
X = -0.2Y-1 + 0.2fxY-1 + 0.4xY-1 + -0.2xFY-1

Reorder the terms:
X = -0.2Y-1 + 0.2fxY-1 + -0.2xFY-1 + 0.4xY-1

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