(Y+1)(y+5)=(y+10)(y-3)

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Solution for (Y+1)(y+5)=(y+10)(y-3) equation: 


Simplifying
(Y + 1)(y + 5) = (y + 10)(y + -3)

Reorder the terms:
(1 + Y)(y + 5) = (y + 10)(y + -3)

Reorder the terms:
(1 + Y)(5 + y) = (y + 10)(y + -3)

Multiply (1 + Y) * (5 + y)
(1(5 + y) + Y(5 + y)) = (y + 10)(y + -3)
((5 * 1 + y * 1) + Y(5 + y)) = (y + 10)(y + -3)
((5 + 1y) + Y(5 + y)) = (y + 10)(y + -3)
(5 + 1y + (5 * Y + y * Y)) = (y + 10)(y + -3)
(5 + 1y + (5Y + yY)) = (y + 10)(y + -3)

Reorder the terms:
(5 + 5Y + 1y + yY) = (y + 10)(y + -3)
(5 + 5Y + 1y + yY) = (y + 10)(y + -3)

Reorder the terms:
5 + 5Y + 1y + yY = (10 + y)(y + -3)

Reorder the terms:
5 + 5Y + 1y + yY = (10 + y)(-3 + y)

Multiply (10 + y) * (-3 + y)
5 + 5Y + 1y + yY = (10(-3 + y) + y(-3 + y))
5 + 5Y + 1y + yY = ((-3 * 10 + y * 10) + y(-3 + y))
5 + 5Y + 1y + yY = ((-30 + 10y) + y(-3 + y))
5 + 5Y + 1y + yY = (-30 + 10y + (-3 * y + y * y))
5 + 5Y + 1y + yY = (-30 + 10y + (-3y + y2))

Combine like terms: 10y + -3y = 7y
5 + 5Y + 1y + yY = (-30 + 7y + y2)

Solving
5 + 5Y + 1y + yY = -30 + 7y + y2

Solving for variable 'Y'.

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

Add '-5' to each side of the equation.
5 + 5Y + 1y + -5 + yY = -30 + 7y + -5 + y2

Reorder the terms:
5 + -5 + 5Y + 1y + yY = -30 + 7y + -5 + y2

Combine like terms: 5 + -5 = 0
0 + 5Y + 1y + yY = -30 + 7y + -5 + y2
5Y + 1y + yY = -30 + 7y + -5 + y2

Reorder the terms:
5Y + 1y + yY = -30 + -5 + 7y + y2

Combine like terms: -30 + -5 = -35
5Y + 1y + yY = -35 + 7y + y2

Add '-1y' to each side of the equation.
5Y + 1y + -1y + yY = -35 + 7y + -1y + y2

Combine like terms: 1y + -1y = 0
5Y + 0 + yY = -35 + 7y + -1y + y2
5Y + yY = -35 + 7y + -1y + y2

Combine like terms: 7y + -1y = 6y
5Y + yY = -35 + 6y + y2

Reorder the terms:
35 + 5Y + -6y + yY + -1y2 = -35 + 6y + y2 + 35 + -6y + -1y2

Reorder the terms:
35 + 5Y + -6y + yY + -1y2 = -35 + 35 + 6y + -6y + y2 + -1y2

Combine like terms: -35 + 35 = 0
35 + 5Y + -6y + yY + -1y2 = 0 + 6y + -6y + y2 + -1y2
35 + 5Y + -6y + yY + -1y2 = 6y + -6y + y2 + -1y2

Combine like terms: 6y + -6y = 0
35 + 5Y + -6y + yY + -1y2 = 0 + y2 + -1y2
35 + 5Y + -6y + yY + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
35 + 5Y + -6y + yY + -1y2 = 0

The solution to this equation could not be determined.

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