(Y+2)(Y+1)=(Y-5)(Y+6)

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Solution for (Y+2)(Y+1)=(Y-5)(Y+6) equation: 


Simplifying
(Y + 2)(Y + 1) = (Y + -5)(Y + 6)

Reorder the terms:
(2 + Y)(Y + 1) = (Y + -5)(Y + 6)

Reorder the terms:
(2 + Y)(1 + Y) = (Y + -5)(Y + 6)

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

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

Reorder the terms:
2 + 3Y + Y2 = (-5 + Y)(Y + 6)

Reorder the terms:
2 + 3Y + Y2 = (-5 + Y)(6 + Y)

Multiply (-5 + Y) * (6 + Y)
2 + 3Y + Y2 = (-5(6 + Y) + Y(6 + Y))
2 + 3Y + Y2 = ((6 * -5 + Y * -5) + Y(6 + Y))
2 + 3Y + Y2 = ((-30 + -5Y) + Y(6 + Y))
2 + 3Y + Y2 = (-30 + -5Y + (6 * Y + Y * Y))
2 + 3Y + Y2 = (-30 + -5Y + (6Y + Y2))

Combine like terms: -5Y + 6Y = 1Y
2 + 3Y + Y2 = (-30 + 1Y + Y2)

Add '-1Y2' to each side of the equation.
2 + 3Y + Y2 + -1Y2 = -30 + 1Y + Y2 + -1Y2

Combine like terms: Y2 + -1Y2 = 0
2 + 3Y + 0 = -30 + 1Y + Y2 + -1Y2
2 + 3Y = -30 + 1Y + Y2 + -1Y2

Combine like terms: Y2 + -1Y2 = 0
2 + 3Y = -30 + 1Y + 0
2 + 3Y = -30 + 1Y

Solving
2 + 3Y = -30 + 1Y

Solving for variable 'Y'.

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

Add '-1Y' to each side of the equation.
2 + 3Y + -1Y = -30 + 1Y + -1Y

Combine like terms: 3Y + -1Y = 2Y
2 + 2Y = -30 + 1Y + -1Y

Combine like terms: 1Y + -1Y = 0
2 + 2Y = -30 + 0
2 + 2Y = -30

Add '-2' to each side of the equation.
2 + -2 + 2Y = -30 + -2

Combine like terms: 2 + -2 = 0
0 + 2Y = -30 + -2
2Y = -30 + -2

Combine like terms: -30 + -2 = -32
2Y = -32

Divide each side by '2'.
Y = -16

Simplifying
Y = -16

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