(2y-10)(y+1)=(y-3)(y-2)

Solution for (2y-10)(y+1)=(y-3)(y-2) equation:

Simplifying
(2y + -10)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-10 + 2y)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-10 + 2y)(1 + y) = (y + -3)(y + -2)

Multiply (-10 + 2y) * (1 + y)
(-10(1 + y) + 2y * (1 + y)) = (y + -3)(y + -2)
((1 * -10 + y * -10) + 2y * (1 + y)) = (y + -3)(y + -2)
((-10 + -10y) + 2y * (1 + y)) = (y + -3)(y + -2)
(-10 + -10y + (1 * 2y + y * 2y)) = (y + -3)(y + -2)
(-10 + -10y + (2y + 2y2)) = (y + -3)(y + -2)

Combine like terms: -10y + 2y = -8y
(-10 + -8y + 2y2) = (y + -3)(y + -2)

Reorder the terms:
-10 + -8y + 2y2 = (-3 + y)(y + -2)

Reorder the terms:
-10 + -8y + 2y2 = (-3 + y)(-2 + y)

Multiply (-3 + y) * (-2 + y)
-10 + -8y + 2y2 = (-3(-2 + y) + y(-2 + y))
-10 + -8y + 2y2 = ((-2 * -3 + y * -3) + y(-2 + y))
-10 + -8y + 2y2 = ((6 + -3y) + y(-2 + y))
-10 + -8y + 2y2 = (6 + -3y + (-2 * y + y * y))
-10 + -8y + 2y2 = (6 + -3y + (-2y + y2))

Combine like terms: -3y + -2y = -5y
-10 + -8y + 2y2 = (6 + -5y + y2)

Solving
-10 + -8y + 2y2 = 6 + -5y + y2

Solving for variable 'y'.

Reorder the terms:
-10 + -6 + -8y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: -10 + -6 = -16
-16 + -8y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: -8y + 5y = -3y
-16 + -3y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-16 + -3y + 1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Reorder the terms:
-16 + -3y + 1y2 = 6 + -6 + -5y + 5y + y2 + -1y2

Combine like terms: 6 + -6 = 0
-16 + -3y + 1y2 = 0 + -5y + 5y + y2 + -1y2
-16 + -3y + 1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
-16 + -3y + 1y2 = 0 + y2 + -1y2
-16 + -3y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-16 + -3y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -3y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -3y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3y + y2 = 0 + 16
-3y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-3y + y2 = 16

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 16 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + -3y + y2 = 18.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(y + -1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
y + -1.5 = 4.272001873

Simplifying
y + -1.5 = 4.272001873

Reorder the terms:
-1.5 + y = 4.272001873

Solving
-1.5 + y = 4.272001873

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 4.272001873 + 1.5
y = 4.272001873 + 1.5

Combine like terms: 4.272001873 + 1.5 = 5.772001873
y = 5.772001873

Simplifying
y = 5.772001873

Subproblem 2
y + -1.5 = -4.272001873

Simplifying
y + -1.5 = -4.272001873

Reorder the terms:
-1.5 + y = -4.272001873

Solving
-1.5 + y = -4.272001873

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -4.272001873 + 1.5
y = -4.272001873 + 1.5

Combine like terms: -4.272001873 + 1.5 = -2.772001873
y = -2.772001873

Simplifying
y = -2.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.772001873, -2.772001873}