(X+3)(3Y-5)=(2Y-1)(3X+4)

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Solution for (X+3)(3Y-5)=(2Y-1)(3X+4) equation: 


Simplifying
(X + 3)(3Y + -5) = (2Y + -1)(3X + 4)

Reorder the terms:
(3 + X)(3Y + -5) = (2Y + -1)(3X + 4)

Reorder the terms:
(3 + X)(-5 + 3Y) = (2Y + -1)(3X + 4)

Multiply (3 + X) * (-5 + 3Y)
(3(-5 + 3Y) + X(-5 + 3Y)) = (2Y + -1)(3X + 4)
((-5 * 3 + 3Y * 3) + X(-5 + 3Y)) = (2Y + -1)(3X + 4)
((-15 + 9Y) + X(-5 + 3Y)) = (2Y + -1)(3X + 4)
(-15 + 9Y + (-5 * X + 3Y * X)) = (2Y + -1)(3X + 4)
(-15 + 9Y + (-5X + 3XY)) = (2Y + -1)(3X + 4)

Reorder the terms:
(-15 + -5X + 3XY + 9Y) = (2Y + -1)(3X + 4)
(-15 + -5X + 3XY + 9Y) = (2Y + -1)(3X + 4)

Reorder the terms:
-15 + -5X + 3XY + 9Y = (-1 + 2Y)(3X + 4)

Reorder the terms:
-15 + -5X + 3XY + 9Y = (-1 + 2Y)(4 + 3X)

Multiply (-1 + 2Y) * (4 + 3X)
-15 + -5X + 3XY + 9Y = (-1(4 + 3X) + 2Y * (4 + 3X))
-15 + -5X + 3XY + 9Y = ((4 * -1 + 3X * -1) + 2Y * (4 + 3X))
-15 + -5X + 3XY + 9Y = ((-4 + -3X) + 2Y * (4 + 3X))
-15 + -5X + 3XY + 9Y = (-4 + -3X + (4 * 2Y + 3X * 2Y))

Reorder the terms:
-15 + -5X + 3XY + 9Y = (-4 + -3X + (6XY + 8Y))
-15 + -5X + 3XY + 9Y = (-4 + -3X + (6XY + 8Y))
-15 + -5X + 3XY + 9Y = (-4 + -3X + 6XY + 8Y)

Solving
-15 + -5X + 3XY + 9Y = -4 + -3X + 6XY + 8Y

Solving for variable 'X'.

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

Add '3X' to each side of the equation.
-15 + -5X + 3XY + 3X + 9Y = -4 + -3X + 6XY + 3X + 8Y

Reorder the terms:
-15 + -5X + 3X + 3XY + 9Y = -4 + -3X + 6XY + 3X + 8Y

Combine like terms: -5X + 3X = -2X
-15 + -2X + 3XY + 9Y = -4 + -3X + 6XY + 3X + 8Y

Reorder the terms:
-15 + -2X + 3XY + 9Y = -4 + -3X + 3X + 6XY + 8Y

Combine like terms: -3X + 3X = 0
-15 + -2X + 3XY + 9Y = -4 + 0 + 6XY + 8Y
-15 + -2X + 3XY + 9Y = -4 + 6XY + 8Y

Add '-6XY' to each side of the equation.
-15 + -2X + 3XY + -6XY + 9Y = -4 + 6XY + -6XY + 8Y

Combine like terms: 3XY + -6XY = -3XY
-15 + -2X + -3XY + 9Y = -4 + 6XY + -6XY + 8Y

Combine like terms: 6XY + -6XY = 0
-15 + -2X + -3XY + 9Y = -4 + 0 + 8Y
-15 + -2X + -3XY + 9Y = -4 + 8Y

Add '15' to each side of the equation.
-15 + -2X + -3XY + 15 + 9Y = -4 + 15 + 8Y

Reorder the terms:
-15 + 15 + -2X + -3XY + 9Y = -4 + 15 + 8Y

Combine like terms: -15 + 15 = 0
0 + -2X + -3XY + 9Y = -4 + 15 + 8Y
-2X + -3XY + 9Y = -4 + 15 + 8Y

Combine like terms: -4 + 15 = 11
-2X + -3XY + 9Y = 11 + 8Y

Add '-9Y' to each side of the equation.
-2X + -3XY + 9Y + -9Y = 11 + 8Y + -9Y

Combine like terms: 9Y + -9Y = 0
-2X + -3XY + 0 = 11 + 8Y + -9Y
-2X + -3XY = 11 + 8Y + -9Y

Combine like terms: 8Y + -9Y = -1Y
-2X + -3XY = 11 + -1Y

Reorder the terms:
-11 + -2X + -3XY + Y = 11 + -1Y + -11 + Y

Reorder the terms:
-11 + -2X + -3XY + Y = 11 + -11 + -1Y + Y

Combine like terms: 11 + -11 = 0
-11 + -2X + -3XY + Y = 0 + -1Y + Y
-11 + -2X + -3XY + Y = -1Y + Y

Combine like terms: -1Y + Y = 0
-11 + -2X + -3XY + Y = 0

The solution to this equation could not be determined.

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