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

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

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

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

Multiply (3 + y) * (6 + 5y)
(3(6 + 5y) + y(6 + 5y)) = 0
((6 * 3 + 5y * 3) + y(6 + 5y)) = 0
((18 + 15y) + y(6 + 5y)) = 0
(18 + 15y + (6 * y + 5y * y)) = 0
(18 + 15y + (6y + 5y2)) = 0

Combine like terms: 15y + 6y = 21y
(18 + 21y + 5y2) = 0

Solving
18 + 21y + 5y2 = 0

Solving for variable 'y'.

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

Simplifying
6 + 5y = 0

Solving
6 + 5y = 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 + 5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5y = 0 + -6
5y = 0 + -6

Combine like terms: 0 + -6 = -6
5y = -6

Divide each side by '5'.
y = -1.2

Simplifying
y = -1.2
Solution
y = {-3, -1.2}