(3y+4)(y+6)=0

Solution for (3y+4)(y+6)=0 equation:

Simplifying
(3y + 4)(y + 6) = 0

Reorder the terms:
(4 + 3y)(y + 6) = 0

Reorder the terms:
(4 + 3y)(6 + y) = 0

Multiply (4 + 3y) * (6 + y)
(4(6 + y) + 3y * (6 + y)) = 0
((6 * 4 + y * 4) + 3y * (6 + y)) = 0
((24 + 4y) + 3y * (6 + y)) = 0
(24 + 4y + (6 * 3y + y * 3y)) = 0
(24 + 4y + (18y + 3y2)) = 0

Combine like terms: 4y + 18y = 22y
(24 + 22y + 3y2) = 0

Solving
24 + 22y + 3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
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 = {-6, -1.333333333}