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

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

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

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

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

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

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

Solving
9 + 9y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(3 + 2y) = 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 '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

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

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-3, -1.5}