3(y+5)(y+4)=-2(3y+5)

Solution for 3(y+5)(y+4)=-2(3y+5) equation:

Simplifying
3(y + 5)(y + 4) = -2(3y + 5)

Reorder the terms:
3(5 + y)(y + 4) = -2(3y + 5)

Reorder the terms:
3(5 + y)(4 + y) = -2(3y + 5)

Multiply (5 + y) * (4 + y)
3(5(4 + y) + y(4 + y)) = -2(3y + 5)
3((4 * 5 + y * 5) + y(4 + y)) = -2(3y + 5)
3((20 + 5y) + y(4 + y)) = -2(3y + 5)
3(20 + 5y + (4 * y + y * y)) = -2(3y + 5)
3(20 + 5y + (4y + y2)) = -2(3y + 5)

Combine like terms: 5y + 4y = 9y
3(20 + 9y + y2) = -2(3y + 5)
(20 * 3 + 9y * 3 + y2 * 3) = -2(3y + 5)
(60 + 27y + 3y2) = -2(3y + 5)

Reorder the terms:
60 + 27y + 3y2 = -2(5 + 3y)
60 + 27y + 3y2 = (5 * -2 + 3y * -2)
60 + 27y + 3y2 = (-10 + -6y)

Solving
60 + 27y + 3y2 = -10 + -6y

Solving for variable 'y'.

Reorder the terms:
60 + 10 + 27y + 6y + 3y2 = -10 + -6y + 10 + 6y

Combine like terms: 60 + 10 = 70
70 + 27y + 6y + 3y2 = -10 + -6y + 10 + 6y

Combine like terms: 27y + 6y = 33y
70 + 33y + 3y2 = -10 + -6y + 10 + 6y

Reorder the terms:
70 + 33y + 3y2 = -10 + 10 + -6y + 6y

Combine like terms: -10 + 10 = 0
70 + 33y + 3y2 = 0 + -6y + 6y
70 + 33y + 3y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
70 + 33y + 3y2 = 0

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

Divide each side by '3'.
23.33333333 + 11y + y2 = 0

Move the constant term to the right:

Add '-23.33333333' to each side of the equation.
23.33333333 + 11y + -23.33333333 + y2 = 0 + -23.33333333

Reorder the terms:
23.33333333 + -23.33333333 + 11y + y2 = 0 + -23.33333333

Combine like terms: 23.33333333 + -23.33333333 = 0.00000000
0.00000000 + 11y + y2 = 0 + -23.33333333
11y + y2 = 0 + -23.33333333

Combine like terms: 0 + -23.33333333 = -23.33333333
11y + y2 = -23.33333333

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = -23.33333333 + 30.25

Reorder the terms:
30.25 + 11y + y2 = -23.33333333 + 30.25

Combine like terms: -23.33333333 + 30.25 = 6.91666667
30.25 + 11y + y2 = 6.91666667

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 6.91666667

Calculate the square root of the right side: 2.62995564

Break this problem into two subproblems by setting 
(y + 5.5) equal to 2.62995564 and -2.62995564.

Subproblem 1
y + 5.5 = 2.62995564

Simplifying
y + 5.5 = 2.62995564

Reorder the terms:
5.5 + y = 2.62995564

Solving
5.5 + y = 2.62995564

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = 2.62995564 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = 2.62995564 + -5.5
y = 2.62995564 + -5.5

Combine like terms: 2.62995564 + -5.5 = -2.87004436
y = -2.87004436

Simplifying
y = -2.87004436

Subproblem 2
y + 5.5 = -2.62995564

Simplifying
y + 5.5 = -2.62995564

Reorder the terms:
5.5 + y = -2.62995564

Solving
5.5 + y = -2.62995564

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = -2.62995564 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = -2.62995564 + -5.5
y = -2.62995564 + -5.5

Combine like terms: -2.62995564 + -5.5 = -8.12995564
y = -8.12995564

Simplifying
y = -8.12995564

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.87004436, -8.12995564}