(3y+7)(6+y)=0

Solution for (3y+7)(6+y)=0 equation:

Simplifying
(3y + 7)(6 + y) = 0

Reorder the terms:
(7 + 3y)(6 + y) = 0

Multiply (7 + 3y) * (6 + y)
(7(6 + y) + 3y * (6 + y)) = 0
((6 * 7 + y * 7) + 3y * (6 + y)) = 0
((42 + 7y) + 3y * (6 + y)) = 0
(42 + 7y + (6 * 3y + y * 3y)) = 0
(42 + 7y + (18y + 3y2)) = 0

Combine like terms: 7y + 18y = 25y
(42 + 25y + 3y2) = 0

Solving
42 + 25y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(7 + 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 '(7 + 3y)' equal to zero and attempt to solve:

Simplifying
7 + 3y = 0

Solving
7 + 3y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3y = 0 + -7
3y = 0 + -7

Combine like terms: 0 + -7 = -7
3y = -7

Divide each side by '3'.
y = -2.333333333

Simplifying
y = -2.333333333
Solution
y = {-6, -2.333333333}