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

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

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

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

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

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

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

Reorder the terms:
-2 + 2y2 = (-3 + y)(y + -2)

Reorder the terms:
-2 + 2y2 = (-3 + y)(-2 + y)

Multiply (-3 + y) * (-2 + y)
-2 + 2y2 = (-3(-2 + y) + y(-2 + y))
-2 + 2y2 = ((-2 * -3 + y * -3) + y(-2 + y))
-2 + 2y2 = ((6 + -3y) + y(-2 + y))
-2 + 2y2 = (6 + -3y + (-2 * y + y * y))
-2 + 2y2 = (6 + -3y + (-2y + y2))

Combine like terms: -3y + -2y = -5y
-2 + 2y2 = (6 + -5y + y2)

Solving
-2 + 2y2 = 6 + -5y + y2

Solving for variable 'y'.

Reorder the terms:
-2 + -6 + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: -2 + -6 = -8
-8 + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-8 + 5y + 1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Reorder the terms:
-8 + 5y + 1y2 = 6 + -6 + -5y + 5y + y2 + -1y2

Combine like terms: 6 + -6 = 0
-8 + 5y + 1y2 = 0 + -5y + 5y + y2 + -1y2
-8 + 5y + 1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
-8 + 5y + 1y2 = 0 + y2 + -1y2
-8 + 5y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-8 + 5y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 5y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + 5y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5y + y2 = 0 + 8
5y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
5y + y2 = 8

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 8 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + 5y + y2 = 14.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
y + 2.5 = 3.774917218

Simplifying
y + 2.5 = 3.774917218

Reorder the terms:
2.5 + y = 3.774917218

Solving
2.5 + y = 3.774917218

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.774917218 + -2.5
y = 3.774917218 + -2.5

Combine like terms: 3.774917218 + -2.5 = 1.274917218
y = 1.274917218

Simplifying
y = 1.274917218

Subproblem 2
y + 2.5 = -3.774917218

Simplifying
y + 2.5 = -3.774917218

Reorder the terms:
2.5 + y = -3.774917218

Solving
2.5 + y = -3.774917218

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.774917218 + -2.5
y = -3.774917218 + -2.5

Combine like terms: -3.774917218 + -2.5 = -6.274917218
y = -6.274917218

Simplifying
y = -6.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.274917218, -6.274917218}