(3y+1)(4+y)=0

Solution for (3y+1)(4+y)=0 equation:

Simplifying
(3y + 1)(4 + y) = 0

Reorder the terms:
(1 + 3y)(4 + y) = 0

Multiply (1 + 3y) * (4 + y)
(1(4 + y) + 3y * (4 + y)) = 0
((4 * 1 + y * 1) + 3y * (4 + y)) = 0
((4 + 1y) + 3y * (4 + y)) = 0
(4 + 1y + (4 * 3y + y * 3y)) = 0
(4 + 1y + (12y + 3y2)) = 0

Combine like terms: 1y + 12y = 13y
(4 + 13y + 3y2) = 0

Solving
4 + 13y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + y)(1 + 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 '(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 = {-4, -0.3333333333}