(3y+5)(6+y)=0

Solution for (3y+5)(6+y)=0 equation:

Simplifying
(3y + 5)(6 + y) = 0

Reorder the terms:
(5 + 3y)(6 + y) = 0

Multiply (5 + 3y) * (6 + y)
(5(6 + y) + 3y * (6 + y)) = 0
((6 * 5 + y * 5) + 3y * (6 + y)) = 0
((30 + 5y) + 3y * (6 + y)) = 0
(30 + 5y + (6 * 3y + y * 3y)) = 0
(30 + 5y + (18y + 3y2)) = 0

Combine like terms: 5y + 18y = 23y
(30 + 23y + 3y2) = 0

Solving
30 + 23y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(5 + 3y) = 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 '(5 + 3y)' equal to zero and attempt to solve:

Simplifying
5 + 3y = 0

Solving
5 + 3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3y = 0 + -5
3y = 0 + -5

Combine like terms: 0 + -5 = -5
3y = -5

Divide each side by '3'.
y = -1.666666667

Simplifying
y = -1.666666667
Solution
y = {-6, -1.666666667}