(y+4)(y+8)=5

Solution for (y+4)(y+8)=5 equation:

Simplifying
(y + 4)(y + 8) = 5

Reorder the terms:
(4 + y)(y + 8) = 5

Reorder the terms:
(4 + y)(8 + y) = 5

Multiply (4 + y) * (8 + y)
(4(8 + y) + y(8 + y)) = 5
((8 * 4 + y * 4) + y(8 + y)) = 5
((32 + 4y) + y(8 + y)) = 5
(32 + 4y + (8 * y + y * y)) = 5
(32 + 4y + (8y + y2)) = 5

Combine like terms: 4y + 8y = 12y
(32 + 12y + y2) = 5

Solving
32 + 12y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
32 + -5 + 12y + y2 = 5 + -5

Combine like terms: 32 + -5 = 27
27 + 12y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
27 + 12y + y2 = 0

Factor a trinomial.
(9 + y)(3 + y) = 0

Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

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

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

Simplifying
y = -3
Solution
y = {-9, -3}