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

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

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

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

Multiply (2 + y) * (3 + 2y)
(2(3 + 2y) + y(3 + 2y)) = 0
((3 * 2 + 2y * 2) + y(3 + 2y)) = 0
((6 + 4y) + y(3 + 2y)) = 0
(6 + 4y + (3 * y + 2y * y)) = 0
(6 + 4y + (3y + 2y2)) = 0

Combine like terms: 4y + 3y = 7y
(6 + 7y + 2y2) = 0

Solving
6 + 7y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + y)(3 + 2y) = 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 '(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 = {-2, -1.5}