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

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


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

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

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

Multiply (-3 + y) * (3 + y)
(-3(3 + y) + y(3 + y)) = (y + -1)(y + -2)
((3 * -3 + y * -3) + y(3 + y)) = (y + -1)(y + -2)
((-9 + -3y) + y(3 + y)) = (y + -1)(y + -2)
(-9 + -3y + (3 * y + y * y)) = (y + -1)(y + -2)
(-9 + -3y + (3y + y2)) = (y + -1)(y + -2)

Combine like terms: -3y + 3y = 0
(-9 + 0 + y2) = (y + -1)(y + -2)
(-9 + y2) = (y + -1)(y + -2)

Reorder the terms:
-9 + y2 = (-1 + y)(y + -2)

Reorder the terms:
-9 + y2 = (-1 + y)(-2 + y)

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

Combine like terms: -1y + -2y = -3y
-9 + y2 = (2 + -3y + y2)

Add '-1y2' to each side of the equation.
-9 + y2 + -1y2 = 2 + -3y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-9 + 0 = 2 + -3y + y2 + -1y2
-9 = 2 + -3y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-9 = 2 + -3y + 0
-9 = 2 + -3y

Solving
-9 = 2 + -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 + 3y = 2 + -3y + 3y

Combine like terms: -3y + 3y = 0
-9 + 3y = 2 + 0
-9 + 3y = 2

Add '9' to each side of the equation.
-9 + 9 + 3y = 2 + 9

Combine like terms: -9 + 9 = 0
0 + 3y = 2 + 9
3y = 2 + 9

Combine like terms: 2 + 9 = 11
3y = 11

Divide each side by '3'.
y = 3.666666667

Simplifying
y = 3.666666667

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