(y+5)(y+10)=-6

Solution for (y+5)(y+10)=-6 equation:

Simplifying
(y + 5)(y + 10) = -6

Reorder the terms:
(5 + y)(y + 10) = -6

Reorder the terms:
(5 + y)(10 + y) = -6

Multiply (5 + y) * (10 + y)
(5(10 + y) + y(10 + y)) = -6
((10 * 5 + y * 5) + y(10 + y)) = -6
((50 + 5y) + y(10 + y)) = -6
(50 + 5y + (10 * y + y * y)) = -6
(50 + 5y + (10y + y2)) = -6

Combine like terms: 5y + 10y = 15y
(50 + 15y + y2) = -6

Solving
50 + 15y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
50 + 6 + 15y + y2 = -6 + 6

Combine like terms: 50 + 6 = 56
56 + 15y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
56 + 15y + y2 = 0

Factor a trinomial.
(8 + y)(7 + y) = 0

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 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 + y = 0 + -8

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

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

Simplifying
y = -8
Subproblem 2
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 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 + y = 0 + -7

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

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

Simplifying
y = -7
Solution
y = {-8, -7}