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

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

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

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

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

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

Combine like terms: 6y + -2y = 4y
1 = (-6 + 4y + 2y2)

Solving
1 = -6 + 4y + 2y2

Solving for variable 'y'.

Combine like terms: 1 + 6 = 7
7 + -4y + -2y2 = -6 + 4y + 2y2 + 6 + -4y + -2y2

Reorder the terms:
7 + -4y + -2y2 = -6 + 6 + 4y + -4y + 2y2 + -2y2

Combine like terms: -6 + 6 = 0
7 + -4y + -2y2 = 0 + 4y + -4y + 2y2 + -2y2
7 + -4y + -2y2 = 4y + -4y + 2y2 + -2y2

Combine like terms: 4y + -4y = 0
7 + -4y + -2y2 = 0 + 2y2 + -2y2
7 + -4y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
7 + -4y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3.5 + 2y + y2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 2y + 3.5 + y2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 2y + y2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 2y + y2 = 0 + 3.5
2y + y2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
2y + y2 = 3.5

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 = 3.5 + 1

Reorder the terms:
1 + 2y + y2 = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
1 + 2y + y2 = 4.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(y + 1) equal to 2.121320344 and -2.121320344.

Subproblem 1
y + 1 = 2.121320344

Simplifying
y + 1 = 2.121320344

Reorder the terms:
1 + y = 2.121320344

Solving
1 + y = 2.121320344

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 = 2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.121320344 + -1
y = 2.121320344 + -1

Combine like terms: 2.121320344 + -1 = 1.121320344
y = 1.121320344

Simplifying
y = 1.121320344

Subproblem 2
y + 1 = -2.121320344

Simplifying
y + 1 = -2.121320344

Reorder the terms:
1 + y = -2.121320344

Solving
1 + y = -2.121320344

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 = -2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.121320344 + -1
y = -2.121320344 + -1

Combine like terms: -2.121320344 + -1 = -3.121320344
y = -3.121320344

Simplifying
y = -3.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.121320344, -3.121320344}