(X+2)(Y-1)=(X+7)(Y-3)

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Solution for (X+2)(Y-1)=(X+7)(Y-3) equation: 


Simplifying
(X + 2)(Y + -1) = (X + 7)(Y + -3)

Reorder the terms:
(2 + X)(Y + -1) = (X + 7)(Y + -3)

Reorder the terms:
(2 + X)(-1 + Y) = (X + 7)(Y + -3)

Multiply (2 + X) * (-1 + Y)
(2(-1 + Y) + X(-1 + Y)) = (X + 7)(Y + -3)
((-1 * 2 + Y * 2) + X(-1 + Y)) = (X + 7)(Y + -3)
((-2 + 2Y) + X(-1 + Y)) = (X + 7)(Y + -3)
(-2 + 2Y + (-1 * X + Y * X)) = (X + 7)(Y + -3)
(-2 + 2Y + (-1X + XY)) = (X + 7)(Y + -3)

Reorder the terms:
(-2 + -1X + XY + 2Y) = (X + 7)(Y + -3)
(-2 + -1X + XY + 2Y) = (X + 7)(Y + -3)

Reorder the terms:
-2 + -1X + XY + 2Y = (7 + X)(Y + -3)

Reorder the terms:
-2 + -1X + XY + 2Y = (7 + X)(-3 + Y)

Multiply (7 + X) * (-3 + Y)
-2 + -1X + XY + 2Y = (7(-3 + Y) + X(-3 + Y))
-2 + -1X + XY + 2Y = ((-3 * 7 + Y * 7) + X(-3 + Y))
-2 + -1X + XY + 2Y = ((-21 + 7Y) + X(-3 + Y))
-2 + -1X + XY + 2Y = (-21 + 7Y + (-3 * X + Y * X))
-2 + -1X + XY + 2Y = (-21 + 7Y + (-3X + XY))

Reorder the terms:
-2 + -1X + XY + 2Y = (-21 + -3X + XY + 7Y)
-2 + -1X + XY + 2Y = (-21 + -3X + XY + 7Y)

Add '-1XY' to each side of the equation.
-2 + -1X + XY + -1XY + 2Y = -21 + -3X + XY + -1XY + 7Y

Combine like terms: XY + -1XY = 0
-2 + -1X + 0 + 2Y = -21 + -3X + XY + -1XY + 7Y
-2 + -1X + 2Y = -21 + -3X + XY + -1XY + 7Y

Combine like terms: XY + -1XY = 0
-2 + -1X + 2Y = -21 + -3X + 0 + 7Y
-2 + -1X + 2Y = -21 + -3X + 7Y

Solving
-2 + -1X + 2Y = -21 + -3X + 7Y

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.
-2 + -1X + 3X + 2Y = -21 + -3X + 3X + 7Y

Combine like terms: -1X + 3X = 2X
-2 + 2X + 2Y = -21 + -3X + 3X + 7Y

Combine like terms: -3X + 3X = 0
-2 + 2X + 2Y = -21 + 0 + 7Y
-2 + 2X + 2Y = -21 + 7Y

Add '2' to each side of the equation.
-2 + 2X + 2 + 2Y = -21 + 2 + 7Y

Reorder the terms:
-2 + 2 + 2X + 2Y = -21 + 2 + 7Y

Combine like terms: -2 + 2 = 0
0 + 2X + 2Y = -21 + 2 + 7Y
2X + 2Y = -21 + 2 + 7Y

Combine like terms: -21 + 2 = -19
2X + 2Y = -19 + 7Y

Add '-2Y' to each side of the equation.
2X + 2Y + -2Y = -19 + 7Y + -2Y

Combine like terms: 2Y + -2Y = 0
2X + 0 = -19 + 7Y + -2Y
2X = -19 + 7Y + -2Y

Combine like terms: 7Y + -2Y = 5Y
2X = -19 + 5Y

Divide each side by '2'.
X = -9.5 + 2.5Y

Simplifying
X = -9.5 + 2.5Y

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