(y-3)(y+6)=(y-5)(y-5)

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Solution for (y-3)(y+6)=(y-5)(y-5) equation: 


Simplifying
(y + -3)(y + 6) = (y + -5)(y + -5)

Reorder the terms:
(-3 + y)(y + 6) = (y + -5)(y + -5)

Reorder the terms:
(-3 + y)(6 + y) = (y + -5)(y + -5)

Multiply (-3 + y) * (6 + y)
(-3(6 + y) + y(6 + y)) = (y + -5)(y + -5)
((6 * -3 + y * -3) + y(6 + y)) = (y + -5)(y + -5)
((-18 + -3y) + y(6 + y)) = (y + -5)(y + -5)
(-18 + -3y + (6 * y + y * y)) = (y + -5)(y + -5)
(-18 + -3y + (6y + y2)) = (y + -5)(y + -5)

Combine like terms: -3y + 6y = 3y
(-18 + 3y + y2) = (y + -5)(y + -5)

Reorder the terms:
-18 + 3y + y2 = (-5 + y)(y + -5)

Reorder the terms:
-18 + 3y + y2 = (-5 + y)(-5 + y)

Multiply (-5 + y) * (-5 + y)
-18 + 3y + y2 = (-5(-5 + y) + y(-5 + y))
-18 + 3y + y2 = ((-5 * -5 + y * -5) + y(-5 + y))
-18 + 3y + y2 = ((25 + -5y) + y(-5 + y))
-18 + 3y + y2 = (25 + -5y + (-5 * y + y * y))
-18 + 3y + y2 = (25 + -5y + (-5y + y2))

Combine like terms: -5y + -5y = -10y
-18 + 3y + y2 = (25 + -10y + y2)

Add '-1y2' to each side of the equation.
-18 + 3y + y2 + -1y2 = 25 + -10y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-18 + 3y + 0 = 25 + -10y + y2 + -1y2
-18 + 3y = 25 + -10y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-18 + 3y = 25 + -10y + 0
-18 + 3y = 25 + -10y

Solving
-18 + 3y = 25 + -10y

Solving for variable 'y'.

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

Add '10y' to each side of the equation.
-18 + 3y + 10y = 25 + -10y + 10y

Combine like terms: 3y + 10y = 13y
-18 + 13y = 25 + -10y + 10y

Combine like terms: -10y + 10y = 0
-18 + 13y = 25 + 0
-18 + 13y = 25

Add '18' to each side of the equation.
-18 + 18 + 13y = 25 + 18

Combine like terms: -18 + 18 = 0
0 + 13y = 25 + 18
13y = 25 + 18

Combine like terms: 25 + 18 = 43
13y = 43

Divide each side by '13'.
y = 3.307692308

Simplifying
y = 3.307692308

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