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

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

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

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

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

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

Solving
3 + 13y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(1 + 4y) = 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 '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 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 + 4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y = 0 + -1
4y = 0 + -1

Combine like terms: 0 + -1 = -1
4y = -1

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {-3, -0.25}