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

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

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

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

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

Multiply (3 + y) * (8 + y)
(3(8 + y) + y(8 + y)) = -6
((8 * 3 + y * 3) + y(8 + y)) = -6
((24 + 3y) + y(8 + y)) = -6
(24 + 3y + (8 * y + y * y)) = -6
(24 + 3y + (8y + y2)) = -6

Combine like terms: 3y + 8y = 11y
(24 + 11y + y2) = -6

Solving
24 + 11y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
24 + 6 + 11y + y2 = -6 + 6

Combine like terms: 24 + 6 = 30
30 + 11y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
30 + 11y + y2 = 0

Factor a trinomial.
(6 + y)(5 + y) = 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 '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {-6, -5}