(y-1)(y+1)-(Y+2)(Y+3)=5y-1

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


Simplifying
(y + -1)(y + 1) + -1(Y + 2)(Y + 3) = 5y + -1

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

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

Multiply (-1 + y) * (1 + y)
(-1(1 + y) + y(1 + y)) + -1(Y + 2)(Y + 3) = 5y + -1
((1 * -1 + y * -1) + y(1 + y)) + -1(Y + 2)(Y + 3) = 5y + -1
((-1 + -1y) + y(1 + y)) + -1(Y + 2)(Y + 3) = 5y + -1
(-1 + -1y + (1 * y + y * y)) + -1(Y + 2)(Y + 3) = 5y + -1
(-1 + -1y + (1y + y2)) + -1(Y + 2)(Y + 3) = 5y + -1

Combine like terms: -1y + 1y = 0
(-1 + 0 + y2) + -1(Y + 2)(Y + 3) = 5y + -1
(-1 + y2) + -1(Y + 2)(Y + 3) = 5y + -1

Reorder the terms:
-1 + y2 + -1(2 + Y)(Y + 3) = 5y + -1

Reorder the terms:
-1 + y2 + -1(2 + Y)(3 + Y) = 5y + -1

Multiply (2 + Y) * (3 + Y)
-1 + y2 + -1(2(3 + Y) + Y(3 + Y)) = 5y + -1
-1 + y2 + -1((3 * 2 + Y * 2) + Y(3 + Y)) = 5y + -1
-1 + y2 + -1((6 + 2Y) + Y(3 + Y)) = 5y + -1
-1 + y2 + -1(6 + 2Y + (3 * Y + Y * Y)) = 5y + -1
-1 + y2 + -1(6 + 2Y + (3Y + Y2)) = 5y + -1

Combine like terms: 2Y + 3Y = 5Y
-1 + y2 + -1(6 + 5Y + Y2) = 5y + -1
-1 + y2 + (6 * -1 + 5Y * -1 + Y2 * -1) = 5y + -1
-1 + y2 + (-6 + -5Y + -1Y2) = 5y + -1

Reorder the terms:
-1 + -6 + -5Y + -1Y2 + y2 = 5y + -1

Combine like terms: -1 + -6 = -7
-7 + -5Y + -1Y2 + y2 = 5y + -1

Reorder the terms:
-7 + -5Y + -1Y2 + y2 = -1 + 5y

Solving
-7 + -5Y + -1Y2 + y2 = -1 + 5y

Solving for variable 'Y'.

Reorder the terms:
-7 + 1 + -5Y + -1Y2 + -5y + y2 = -1 + 5y + 1 + -5y

Combine like terms: -7 + 1 = -6
-6 + -5Y + -1Y2 + -5y + y2 = -1 + 5y + 1 + -5y

Reorder the terms:
-6 + -5Y + -1Y2 + -5y + y2 = -1 + 1 + 5y + -5y

Combine like terms: -1 + 1 = 0
-6 + -5Y + -1Y2 + -5y + y2 = 0 + 5y + -5y
-6 + -5Y + -1Y2 + -5y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-6 + -5Y + -1Y2 + -5y + y2 = 0

The solution to this equation could not be determined.

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