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

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

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

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

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

Multiply (2 + 3y) * (2 + y)
(2(2 + y) + 3y * (2 + y)) = -3(y + 2)
((2 * 2 + y * 2) + 3y * (2 + y)) = -3(y + 2)
((4 + 2y) + 3y * (2 + y)) = -3(y + 2)
(4 + 2y + (2 * 3y + y * 3y)) = -3(y + 2)
(4 + 2y + (6y + 3y2)) = -3(y + 2)

Combine like terms: 2y + 6y = 8y
(4 + 8y + 3y2) = -3(y + 2)

Reorder the terms:
4 + 8y + 3y2 = -3(2 + y)
4 + 8y + 3y2 = (2 * -3 + y * -3)
4 + 8y + 3y2 = (-6 + -3y)

Solving
4 + 8y + 3y2 = -6 + -3y

Solving for variable 'y'.

Reorder the terms:
4 + 6 + 8y + 3y + 3y2 = -6 + -3y + 6 + 3y

Combine like terms: 4 + 6 = 10
10 + 8y + 3y + 3y2 = -6 + -3y + 6 + 3y

Combine like terms: 8y + 3y = 11y
10 + 11y + 3y2 = -6 + -3y + 6 + 3y

Reorder the terms:
10 + 11y + 3y2 = -6 + 6 + -3y + 3y

Combine like terms: -6 + 6 = 0
10 + 11y + 3y2 = 0 + -3y + 3y
10 + 11y + 3y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
10 + 11y + 3y2 = 0

Factor a trinomial.
(2 + y)(5 + 3y) = 0

Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(5 + 3y)' equal to zero and attempt to solve:

Simplifying
5 + 3y = 0

Solving
5 + 3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3y = 0 + -5
3y = 0 + -5

Combine like terms: 0 + -5 = -5
3y = -5

Divide each side by '3'.
y = -1.666666667

Simplifying
y = -1.666666667
Solution
y = {-2, -1.666666667}