y+3-(y+1)(y+2)=0

Solution for y+3-(y+1)(y+2)=0 equation:

Simplifying
y + 3 + -1(y + 1)(y + 2) = 0

Reorder the terms:
y + 3 + -1(1 + y)(y + 2) = 0

Reorder the terms:
y + 3 + -1(1 + y)(2 + y) = 0

Multiply (1 + y) * (2 + y)
y + 3 + -1(1(2 + y) + y(2 + y)) = 0
y + 3 + -1((2 * 1 + y * 1) + y(2 + y)) = 0
y + 3 + -1((2 + 1y) + y(2 + y)) = 0
y + 3 + -1(2 + 1y + (2 * y + y * y)) = 0
y + 3 + -1(2 + 1y + (2y + y2)) = 0

Combine like terms: 1y + 2y = 3y
y + 3 + -1(2 + 3y + y2) = 0
y + 3 + (2 * -1 + 3y * -1 + y2 * -1) = 0
y + 3 + (-2 + -3y + -1y2) = 0

Reorder the terms:
3 + -2 + y + -3y + -1y2 = 0

Combine like terms: 3 + -2 = 1
1 + y + -3y + -1y2 = 0

Combine like terms: y + -3y = -2y
1 + -2y + -1y2 = 0

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

Solving for variable 'y'.

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

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

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 2y + y2 = 0 + 1

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

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

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
y + 1 = 1.414213562

Simplifying
y + 1 = 1.414213562

Reorder the terms:
1 + y = 1.414213562

Solving
1 + y = 1.414213562

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 = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.414213562 + -1
y = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
y = 0.414213562

Simplifying
y = 0.414213562

Subproblem 2
y + 1 = -1.414213562

Simplifying
y + 1 = -1.414213562

Reorder the terms:
1 + y = -1.414213562

Solving
1 + y = -1.414213562

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 = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.414213562 + -1
y = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
y = -2.414213562

Simplifying
y = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.414213562, -2.414213562}