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

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

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

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

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

Combine like terms: 18y + 4y = 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}