(3y+1)(2y+4)=0

Solution for (3y+1)(2y+4)=0 equation:

Simplifying
(3y + 1)(2y + 4) = 0

Reorder the terms:
(1 + 3y)(2y + 4) = 0

Reorder the terms:
(1 + 3y)(4 + 2y) = 0

Multiply (1 + 3y) * (4 + 2y)
(1(4 + 2y) + 3y * (4 + 2y)) = 0
((4 * 1 + 2y * 1) + 3y * (4 + 2y)) = 0
((4 + 2y) + 3y * (4 + 2y)) = 0
(4 + 2y + (4 * 3y + 2y * 3y)) = 0
(4 + 2y + (12y + 6y2)) = 0

Combine like terms: 2y + 12y = 14y
(4 + 14y + 6y2) = 0

Solving
4 + 14y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 7y + 3y2) = 0

Factor a trinomial.
2((2 + y)(1 + 3y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
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 = {-2, -0.3333333333}