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

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

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

Combine like terms: y + -2y = -1y
-1y = (y + -2)(y + 3)

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

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

Multiply (-2 + y) * (3 + y)
-1y = (-2(3 + y) + y(3 + y))
-1y = ((3 * -2 + y * -2) + y(3 + y))
-1y = ((-6 + -2y) + y(3 + y))
-1y = (-6 + -2y + (3 * y + y * y))
-1y = (-6 + -2y + (3y + y2))

Combine like terms: -2y + 3y = 1y
-1y = (-6 + 1y + y2)

Solving
-1y = -6 + 1y + y2

Solving for variable 'y'.

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

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

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

Combine like terms: -6 + 6 = 0
6 + -2y + -1y2 = 0 + 1y + -1y + y2 + -1y2
6 + -2y + -1y2 = 1y + -1y + y2 + -1y2

Combine like terms: 1y + -1y = 0
6 + -2y + -1y2 = 0 + y2 + -1y2
6 + -2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -2y + -1y2 = 0

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

Divide each side by '-1'.
-6 + 2y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 2y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2y + y2 = 0 + 6
2y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
2y + y2 = 6

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 6 + 1

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

Combine like terms: 6 + 1 = 7
1 + 2y + y2 = 7

Factor a perfect square on the left side:
(y + 1)(y + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
y + 1 = 2.645751311

Simplifying
y + 1 = 2.645751311

Reorder the terms:
1 + y = 2.645751311

Solving
1 + y = 2.645751311

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.645751311 + -1
y = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
y = 1.645751311

Simplifying
y = 1.645751311

Subproblem 2
y + 1 = -2.645751311

Simplifying
y + 1 = -2.645751311

Reorder the terms:
1 + y = -2.645751311

Solving
1 + y = -2.645751311

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.645751311 + -1
y = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
y = -3.645751311

Simplifying
y = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.645751311, -3.645751311}