(3y+8)(6+y)=0

Solution for (3y+8)(6+y)=0 equation:

Simplifying
(3y + 8)(6 + y) = 0

Reorder the terms:
(8 + 3y)(6 + y) = 0

Multiply (8 + 3y) * (6 + y)
(8(6 + y) + 3y * (6 + y)) = 0
((6 * 8 + y * 8) + 3y * (6 + y)) = 0
((48 + 8y) + 3y * (6 + y)) = 0
(48 + 8y + (6 * 3y + y * 3y)) = 0
(48 + 8y + (18y + 3y2)) = 0

Combine like terms: 8y + 18y = 26y
(48 + 26y + 3y2) = 0

Solving
48 + 26y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(8 + 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 '(8 + 3y)' equal to zero and attempt to solve:

Simplifying
8 + 3y = 0

Solving
8 + 3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3y = 0 + -8
3y = 0 + -8

Combine like terms: 0 + -8 = -8
3y = -8

Divide each side by '3'.
y = -2.666666667

Simplifying
y = -2.666666667
Solution
y = {-6, -2.666666667}