(y-1)(8-y)=16-(y-2)

Solution for (y-1)(8-y)=16-(y-2) equation:

Simplifying
(y + -1)(8 + -1y) = 16 + -1(y + -2)

Reorder the terms:
(-1 + y)(8 + -1y) = 16 + -1(y + -2)

Multiply (-1 + y) * (8 + -1y)
(-1(8 + -1y) + y(8 + -1y)) = 16 + -1(y + -2)
((8 * -1 + -1y * -1) + y(8 + -1y)) = 16 + -1(y + -2)
((-8 + 1y) + y(8 + -1y)) = 16 + -1(y + -2)
(-8 + 1y + (8 * y + -1y * y)) = 16 + -1(y + -2)
(-8 + 1y + (8y + -1y2)) = 16 + -1(y + -2)

Combine like terms: 1y + 8y = 9y
(-8 + 9y + -1y2) = 16 + -1(y + -2)

Reorder the terms:
-8 + 9y + -1y2 = 16 + -1(-2 + y)
-8 + 9y + -1y2 = 16 + (-2 * -1 + y * -1)
-8 + 9y + -1y2 = 16 + (2 + -1y)

Combine like terms: 16 + 2 = 18
-8 + 9y + -1y2 = 18 + -1y

Solving
-8 + 9y + -1y2 = 18 + -1y

Solving for variable 'y'.

Reorder the terms:
-8 + -18 + 9y + y + -1y2 = 18 + -1y + -18 + y

Combine like terms: -8 + -18 = -26
-26 + 9y + y + -1y2 = 18 + -1y + -18 + y

Combine like terms: 9y + y = 10y
-26 + 10y + -1y2 = 18 + -1y + -18 + y

Reorder the terms:
-26 + 10y + -1y2 = 18 + -18 + -1y + y

Combine like terms: 18 + -18 = 0
-26 + 10y + -1y2 = 0 + -1y + y
-26 + 10y + -1y2 = -1y + y

Combine like terms: -1y + y = 0
-26 + 10y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
26 + -10y + y2 = 0

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -10y + -26 + y2 = 0 + -26

Reorder the terms:
26 + -26 + -10y + y2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -10y + y2 = 0 + -26
-10y + y2 = 0 + -26

Combine like terms: 0 + -26 = -26
-10y + y2 = -26

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = -26 + 25

Reorder the terms:
25 + -10y + y2 = -26 + 25

Combine like terms: -26 + 25 = -1
25 + -10y + y2 = -1

Factor a perfect square on the left side:
(y + -5)(y + -5) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.