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

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

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

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

Multiply (2 + 3y) * (3 + y)
(2(3 + y) + 3y * (3 + y)) = 0
((3 * 2 + y * 2) + 3y * (3 + y)) = 0
((6 + 2y) + 3y * (3 + y)) = 0
(6 + 2y + (3 * 3y + y * 3y)) = 0
(6 + 2y + (9y + 3y2)) = 0

Combine like terms: 2y + 9y = 11y
(6 + 11y + 3y2) = 0

Solving
6 + 11y + 3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

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

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

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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

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

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

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-3, -0.6666666667}