(2y+6)(y+1)=0

Solution for (2y+6)(y+1)=0 equation:

Simplifying
(2y + 6)(y + 1) = 0

Reorder the terms:
(6 + 2y)(y + 1) = 0

Reorder the terms:
(6 + 2y)(1 + y) = 0

Multiply (6 + 2y) * (1 + y)
(6(1 + y) + 2y * (1 + y)) = 0
((1 * 6 + y * 6) + 2y * (1 + y)) = 0
((6 + 6y) + 2y * (1 + y)) = 0
(6 + 6y + (1 * 2y + y * 2y)) = 0
(6 + 6y + (2y + 2y2)) = 0

Combine like terms: 6y + 2y = 8y
(6 + 8y + 2y2) = 0

Solving
6 + 8y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4y + y2) = 0

Factor a trinomial.
2((3 + y)(1 + y)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

Add '-1' to each side of the equation.
1 + -1 + y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y = 0 + -1
y = 0 + -1

Combine like terms: 0 + -1 = -1
y = -1

Simplifying
y = -1
Solution
y = {-3, -1}