(2x-1)(y+1)=(y-3)(y-2)

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Solution for (2x-1)(y+1)=(y-3)(y-2) equation: 


Simplifying
(2x + -1)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-1 + 2x)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-1 + 2x)(1 + y) = (y + -3)(y + -2)

Multiply (-1 + 2x) * (1 + y)
(-1(1 + y) + 2x * (1 + y)) = (y + -3)(y + -2)
((1 * -1 + y * -1) + 2x * (1 + y)) = (y + -3)(y + -2)
((-1 + -1y) + 2x * (1 + y)) = (y + -3)(y + -2)
(-1 + -1y + (1 * 2x + y * 2x)) = (y + -3)(y + -2)
(-1 + -1y + (2x + 2xy)) = (y + -3)(y + -2)

Reorder the terms:
(-1 + 2x + 2xy + -1y) = (y + -3)(y + -2)
(-1 + 2x + 2xy + -1y) = (y + -3)(y + -2)

Reorder the terms:
-1 + 2x + 2xy + -1y = (-3 + y)(y + -2)

Reorder the terms:
-1 + 2x + 2xy + -1y = (-3 + y)(-2 + y)

Multiply (-3 + y) * (-2 + y)
-1 + 2x + 2xy + -1y = (-3(-2 + y) + y(-2 + y))
-1 + 2x + 2xy + -1y = ((-2 * -3 + y * -3) + y(-2 + y))
-1 + 2x + 2xy + -1y = ((6 + -3y) + y(-2 + y))
-1 + 2x + 2xy + -1y = (6 + -3y + (-2 * y + y * y))
-1 + 2x + 2xy + -1y = (6 + -3y + (-2y + y2))

Combine like terms: -3y + -2y = -5y
-1 + 2x + 2xy + -1y = (6 + -5y + y2)

Solving
-1 + 2x + 2xy + -1y = 6 + -5y + y2

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 2x + 2xy + 1 + -1y = 6 + -5y + 1 + y2

Reorder the terms:
-1 + 1 + 2x + 2xy + -1y = 6 + -5y + 1 + y2

Combine like terms: -1 + 1 = 0
0 + 2x + 2xy + -1y = 6 + -5y + 1 + y2
2x + 2xy + -1y = 6 + -5y + 1 + y2

Reorder the terms:
2x + 2xy + -1y = 6 + 1 + -5y + y2

Combine like terms: 6 + 1 = 7
2x + 2xy + -1y = 7 + -5y + y2

Add 'y' to each side of the equation.
2x + 2xy + -1y + y = 7 + -5y + y + y2

Combine like terms: -1y + y = 0
2x + 2xy + 0 = 7 + -5y + y + y2
2x + 2xy = 7 + -5y + y + y2

Combine like terms: -5y + y = -4y
2x + 2xy = 7 + -4y + y2

Reorder the terms:
-7 + 2x + 2xy + 4y + -1y2 = 7 + -4y + y2 + -7 + 4y + -1y2

Reorder the terms:
-7 + 2x + 2xy + 4y + -1y2 = 7 + -7 + -4y + 4y + y2 + -1y2

Combine like terms: 7 + -7 = 0
-7 + 2x + 2xy + 4y + -1y2 = 0 + -4y + 4y + y2 + -1y2
-7 + 2x + 2xy + 4y + -1y2 = -4y + 4y + y2 + -1y2

Combine like terms: -4y + 4y = 0
-7 + 2x + 2xy + 4y + -1y2 = 0 + y2 + -1y2
-7 + 2x + 2xy + 4y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-7 + 2x + 2xy + 4y + -1y2 = 0

The solution to this equation could not be determined.

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