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

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

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

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

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

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

Combine like terms: 6y + -2y = 4y
2 = (-6 + 4y + 2y2)

Solving
2 = -6 + 4y + 2y2

Solving for variable 'y'.

Combine like terms: 2 + 6 = 8
8 + -4y + -2y2 = -6 + 4y + 2y2 + 6 + -4y + -2y2

Reorder the terms:
8 + -4y + -2y2 = -6 + 6 + 4y + -4y + 2y2 + -2y2

Combine like terms: -6 + 6 = 0
8 + -4y + -2y2 = 0 + 4y + -4y + 2y2 + -2y2
8 + -4y + -2y2 = 4y + -4y + 2y2 + -2y2

Combine like terms: 4y + -4y = 0
8 + -4y + -2y2 = 0 + 2y2 + -2y2
8 + -4y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
8 + -4y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -2y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -2y + -1y2)' equal to zero and attempt to solve:

Simplifying
4 + -2y + -1y2 = 0

Solving
4 + -2y + -1y2 = 0

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

Divide each side by '-1'.
-4 + 2y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 2y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2y + y2 = 0 + 4
2y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
2y + y2 = 4

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 = 4 + 1

Reorder the terms:
1 + 2y + y2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2y + y2 = 5

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

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
y + 1 = 2.236067978

Simplifying
y + 1 = 2.236067978

Reorder the terms:
1 + y = 2.236067978

Solving
1 + y = 2.236067978

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 = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.236067978 + -1
y = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
y = 1.236067978

Simplifying
y = 1.236067978

Subproblem 2
y + 1 = -2.236067978

Simplifying
y + 1 = -2.236067978

Reorder the terms:
1 + y = -2.236067978

Solving
1 + y = -2.236067978

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 = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.236067978 + -1
y = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
y = -3.236067978

Simplifying
y = -3.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.236067978, -3.236067978}
Solution
y = {1.236067978, -3.236067978}