(3y+1)(y+5)=-11

Solution for (3y+1)(y+5)=-11 equation:

Simplifying
(3y + 1)(y + 5) = -11

Reorder the terms:
(1 + 3y)(y + 5) = -11

Reorder the terms:
(1 + 3y)(5 + y) = -11

Multiply (1 + 3y) * (5 + y)
(1(5 + y) + 3y * (5 + y)) = -11
((5 * 1 + y * 1) + 3y * (5 + y)) = -11
((5 + 1y) + 3y * (5 + y)) = -11
(5 + 1y + (5 * 3y + y * 3y)) = -11
(5 + 1y + (15y + 3y2)) = -11

Combine like terms: 1y + 15y = 16y
(5 + 16y + 3y2) = -11

Solving
5 + 16y + 3y2 = -11

Solving for variable 'y'.

Reorder the terms:
5 + 11 + 16y + 3y2 = -11 + 11

Combine like terms: 5 + 11 = 16
16 + 16y + 3y2 = -11 + 11

Combine like terms: -11 + 11 = 0
16 + 16y + 3y2 = 0

Factor a trinomial.
(4 + y)(4 + 3y) = 0

Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {-4, -1.333333333}