2(y+4)+3(y+3)=(y+3)(y-1)

Solution for 2(y+4)+3(y+3)=(y+3)(y-1) equation:

Simplifying
2(y + 4) + 3(y + 3) = (y + 3)(y + -1)

Reorder the terms:
2(4 + y) + 3(y + 3) = (y + 3)(y + -1)
(4 * 2 + y * 2) + 3(y + 3) = (y + 3)(y + -1)
(8 + 2y) + 3(y + 3) = (y + 3)(y + -1)

Reorder the terms:
8 + 2y + 3(3 + y) = (y + 3)(y + -1)
8 + 2y + (3 * 3 + y * 3) = (y + 3)(y + -1)
8 + 2y + (9 + 3y) = (y + 3)(y + -1)

Reorder the terms:
8 + 9 + 2y + 3y = (y + 3)(y + -1)

Combine like terms: 8 + 9 = 17
17 + 2y + 3y = (y + 3)(y + -1)

Combine like terms: 2y + 3y = 5y
17 + 5y = (y + 3)(y + -1)

Reorder the terms:
17 + 5y = (3 + y)(y + -1)

Reorder the terms:
17 + 5y = (3 + y)(-1 + y)

Multiply (3 + y) * (-1 + y)
17 + 5y = (3(-1 + y) + y(-1 + y))
17 + 5y = ((-1 * 3 + y * 3) + y(-1 + y))
17 + 5y = ((-3 + 3y) + y(-1 + y))
17 + 5y = (-3 + 3y + (-1 * y + y * y))
17 + 5y = (-3 + 3y + (-1y + y2))

Combine like terms: 3y + -1y = 2y
17 + 5y = (-3 + 2y + y2)

Solving
17 + 5y = -3 + 2y + y2

Solving for variable 'y'.

Reorder the terms:
17 + 3 + 5y + -2y + -1y2 = -3 + 2y + y2 + 3 + -2y + -1y2

Combine like terms: 17 + 3 = 20
20 + 5y + -2y + -1y2 = -3 + 2y + y2 + 3 + -2y + -1y2

Combine like terms: 5y + -2y = 3y
20 + 3y + -1y2 = -3 + 2y + y2 + 3 + -2y + -1y2

Reorder the terms:
20 + 3y + -1y2 = -3 + 3 + 2y + -2y + y2 + -1y2

Combine like terms: -3 + 3 = 0
20 + 3y + -1y2 = 0 + 2y + -2y + y2 + -1y2
20 + 3y + -1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
20 + 3y + -1y2 = 0 + y2 + -1y2
20 + 3y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
20 + 3y + -1y2 = 0

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

Divide each side by '-1'.
-20 + -3y + y2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -3y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + -3y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3y + y2 = 0 + 20
-3y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
-3y + y2 = 20

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 = 20 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + -3y + y2 = 22.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + -1.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
y + -1.5 = 4.716990566

Simplifying
y + -1.5 = 4.716990566

Reorder the terms:
-1.5 + y = 4.716990566

Solving
-1.5 + y = 4.716990566

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 = 4.716990566 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 4.716990566 + 1.5
y = 4.716990566 + 1.5

Combine like terms: 4.716990566 + 1.5 = 6.216990566
y = 6.216990566

Simplifying
y = 6.216990566

Subproblem 2
y + -1.5 = -4.716990566

Simplifying
y + -1.5 = -4.716990566

Reorder the terms:
-1.5 + y = -4.716990566

Solving
-1.5 + y = -4.716990566

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 = -4.716990566 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -4.716990566 + 1.5
y = -4.716990566 + 1.5

Combine like terms: -4.716990566 + 1.5 = -3.216990566
y = -3.216990566

Simplifying
y = -3.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.216990566, -3.216990566}