(y-5)(y-1)-y=-13

Solution for (y-5)(y-1)-y=-13 equation:

Simplifying
(y + -5)(y + -1) + -1y = -13

Reorder the terms:
(-5 + y)(y + -1) + -1y = -13

Reorder the terms:
(-5 + y)(-1 + y) + -1y = -13

Multiply (-5 + y) * (-1 + y)
(-5(-1 + y) + y(-1 + y)) + -1y = -13
((-1 * -5 + y * -5) + y(-1 + y)) + -1y = -13
((5 + -5y) + y(-1 + y)) + -1y = -13
(5 + -5y + (-1 * y + y * y)) + -1y = -13
(5 + -5y + (-1y + y2)) + -1y = -13

Combine like terms: -5y + -1y = -6y
(5 + -6y + y2) + -1y = -13

Reorder the terms:
5 + -6y + -1y + y2 = -13

Combine like terms: -6y + -1y = -7y
5 + -7y + y2 = -13

Solving
5 + -7y + y2 = -13

Solving for variable 'y'.

Reorder the terms:
5 + 13 + -7y + y2 = -13 + 13

Combine like terms: 5 + 13 = 18
18 + -7y + y2 = -13 + 13

Combine like terms: -13 + 13 = 0
18 + -7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -7y + -18 + y2 = 0 + -18

Reorder the terms:
18 + -18 + -7y + y2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -7y + y2 = 0 + -18
-7y + y2 = 0 + -18

Combine like terms: 0 + -18 = -18
-7y + y2 = -18

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -18 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -18 + 12.25

Combine like terms: -18 + 12.25 = -5.75
12.25 + -7y + y2 = -5.75

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.