(y+6)(y+1)=-6

Solution for (y+6)(y+1)=-6 equation:

Simplifying
(y + 6)(y + 1) = -6

Reorder the terms:
(6 + y)(y + 1) = -6

Reorder the terms:
(6 + y)(1 + y) = -6

Multiply (6 + y) * (1 + y)
(6(1 + y) + y(1 + y)) = -6
((1 * 6 + y * 6) + y(1 + y)) = -6
((6 + 6y) + y(1 + y)) = -6
(6 + 6y + (1 * y + y * y)) = -6
(6 + 6y + (1y + y2)) = -6

Combine like terms: 6y + 1y = 7y
(6 + 7y + y2) = -6

Solving
6 + 7y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
6 + 6 + 7y + y2 = -6 + 6

Combine like terms: 6 + 6 = 12
12 + 7y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
12 + 7y + y2 = 0

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

Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
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 = {-4, -3}