(3y+1)(5+y)=0

Solution for (3y+1)(5+y)=0 equation:

Simplifying
(3y + 1)(5 + y) = 0

Reorder the terms:
(1 + 3y)(5 + y) = 0

Multiply (1 + 3y) * (5 + y)
(1(5 + y) + 3y * (5 + y)) = 0
((5 * 1 + y * 1) + 3y * (5 + y)) = 0
((5 + 1y) + 3y * (5 + y)) = 0
(5 + 1y + (5 * 3y + y * 3y)) = 0
(5 + 1y + (15y + 3y2)) = 0

Combine like terms: 1y + 15y = 16y
(5 + 16y + 3y2) = 0

Solving
5 + 16y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(1 + 3y) = 0

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5
Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {-5, -0.3333333333}