(y+1)(y-9)=(y+5)(y-2)

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Solution for (y+1)(y-9)=(y+5)(y-2) equation: 


Simplifying
(y + 1)(y + -9) = (y + 5)(y + -2)

Reorder the terms:
(1 + y)(y + -9) = (y + 5)(y + -2)

Reorder the terms:
(1 + y)(-9 + y) = (y + 5)(y + -2)

Multiply (1 + y) * (-9 + y)
(1(-9 + y) + y(-9 + y)) = (y + 5)(y + -2)
((-9 * 1 + y * 1) + y(-9 + y)) = (y + 5)(y + -2)
((-9 + 1y) + y(-9 + y)) = (y + 5)(y + -2)
(-9 + 1y + (-9 * y + y * y)) = (y + 5)(y + -2)
(-9 + 1y + (-9y + y2)) = (y + 5)(y + -2)

Combine like terms: 1y + -9y = -8y
(-9 + -8y + y2) = (y + 5)(y + -2)

Reorder the terms:
-9 + -8y + y2 = (5 + y)(y + -2)

Reorder the terms:
-9 + -8y + y2 = (5 + y)(-2 + y)

Multiply (5 + y) * (-2 + y)
-9 + -8y + y2 = (5(-2 + y) + y(-2 + y))
-9 + -8y + y2 = ((-2 * 5 + y * 5) + y(-2 + y))
-9 + -8y + y2 = ((-10 + 5y) + y(-2 + y))
-9 + -8y + y2 = (-10 + 5y + (-2 * y + y * y))
-9 + -8y + y2 = (-10 + 5y + (-2y + y2))

Combine like terms: 5y + -2y = 3y
-9 + -8y + y2 = (-10 + 3y + y2)

Add '-1y2' to each side of the equation.
-9 + -8y + y2 + -1y2 = -10 + 3y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-9 + -8y + 0 = -10 + 3y + y2 + -1y2
-9 + -8y = -10 + 3y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-9 + -8y = -10 + 3y + 0
-9 + -8y = -10 + 3y

Solving
-9 + -8y = -10 + 3y

Solving for variable 'y'.

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

Add '-3y' to each side of the equation.
-9 + -8y + -3y = -10 + 3y + -3y

Combine like terms: -8y + -3y = -11y
-9 + -11y = -10 + 3y + -3y

Combine like terms: 3y + -3y = 0
-9 + -11y = -10 + 0
-9 + -11y = -10

Add '9' to each side of the equation.
-9 + 9 + -11y = -10 + 9

Combine like terms: -9 + 9 = 0
0 + -11y = -10 + 9
-11y = -10 + 9

Combine like terms: -10 + 9 = -1
-11y = -1

Divide each side by '-11'.
y = 0.09090909091

Simplifying
y = 0.09090909091

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