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

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

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

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

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

Combine like terms: 3y + 12y = 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}