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

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


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

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

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

Multiply (1 + Y) * (3 + y)
(1(3 + y) + Y(3 + y)) = (y + 2)(y + -7) + -1
((3 * 1 + y * 1) + Y(3 + y)) = (y + 2)(y + -7) + -1
((3 + 1y) + Y(3 + y)) = (y + 2)(y + -7) + -1
(3 + 1y + (3 * Y + y * Y)) = (y + 2)(y + -7) + -1
(3 + 1y + (3Y + yY)) = (y + 2)(y + -7) + -1

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

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

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

Multiply (2 + y) * (-7 + y)
3 + 3Y + 1y + yY = (2(-7 + y) + y(-7 + y)) + -1
3 + 3Y + 1y + yY = ((-7 * 2 + y * 2) + y(-7 + y)) + -1
3 + 3Y + 1y + yY = ((-14 + 2y) + y(-7 + y)) + -1
3 + 3Y + 1y + yY = (-14 + 2y + (-7 * y + y * y)) + -1
3 + 3Y + 1y + yY = (-14 + 2y + (-7y + y2)) + -1

Combine like terms: 2y + -7y = -5y
3 + 3Y + 1y + yY = (-14 + -5y + y2) + -1

Reorder the terms:
3 + 3Y + 1y + yY = -14 + -1 + -5y + y2

Combine like terms: -14 + -1 = -15
3 + 3Y + 1y + yY = -15 + -5y + y2

Solving
3 + 3Y + 1y + yY = -15 + -5y + y2

Solving for variable 'Y'.

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

Add '-3' to each side of the equation.
3 + 3Y + 1y + -3 + yY = -15 + -5y + -3 + y2

Reorder the terms:
3 + -3 + 3Y + 1y + yY = -15 + -5y + -3 + y2

Combine like terms: 3 + -3 = 0
0 + 3Y + 1y + yY = -15 + -5y + -3 + y2
3Y + 1y + yY = -15 + -5y + -3 + y2

Reorder the terms:
3Y + 1y + yY = -15 + -3 + -5y + y2

Combine like terms: -15 + -3 = -18
3Y + 1y + yY = -18 + -5y + y2

Add '-1y' to each side of the equation.
3Y + 1y + -1y + yY = -18 + -5y + -1y + y2

Combine like terms: 1y + -1y = 0
3Y + 0 + yY = -18 + -5y + -1y + y2
3Y + yY = -18 + -5y + -1y + y2

Combine like terms: -5y + -1y = -6y
3Y + yY = -18 + -6y + y2

Reorder the terms:
18 + 3Y + 6y + yY + -1y2 = -18 + -6y + y2 + 18 + 6y + -1y2

Reorder the terms:
18 + 3Y + 6y + yY + -1y2 = -18 + 18 + -6y + 6y + y2 + -1y2

Combine like terms: -18 + 18 = 0
18 + 3Y + 6y + yY + -1y2 = 0 + -6y + 6y + y2 + -1y2
18 + 3Y + 6y + yY + -1y2 = -6y + 6y + y2 + -1y2

Combine like terms: -6y + 6y = 0
18 + 3Y + 6y + yY + -1y2 = 0 + y2 + -1y2
18 + 3Y + 6y + yY + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
18 + 3Y + 6y + yY + -1y2 = 0

The solution to this equation could not be determined.

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