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

Solution for (6+y)(2y+3)=0 equation:

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

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

Multiply (6 + y) * (3 + 2y)
(6(3 + 2y) + y(3 + 2y)) = 0
((3 * 6 + 2y * 6) + y(3 + 2y)) = 0
((18 + 12y) + y(3 + 2y)) = 0
(18 + 12y + (3 * y + 2y * y)) = 0
(18 + 12y + (3y + 2y2)) = 0

Combine like terms: 12y + 3y = 15y
(18 + 15y + 2y2) = 0

Solving
18 + 15y + 2y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
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 = {-6, -1.5}