(y+6)(y+3)=0

Solution for (y+6)(y+3)=0 equation:

Simplifying
(y + 6)(y + 3) = 0

Reorder the terms:
(6 + y)(y + 3) = 0

Reorder the terms:
(6 + y)(3 + y) = 0

Multiply (6 + y) * (3 + y)
(6(3 + y) + y(3 + y)) = 0
((3 * 6 + y * 6) + y(3 + y)) = 0
((18 + 6y) + y(3 + y)) = 0
(18 + 6y + (3 * y + y * y)) = 0
(18 + 6y + (3y + y2)) = 0

Combine like terms: 6y + 3y = 9y
(18 + 9y + y2) = 0

Solving
18 + 9y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(3 + 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 '(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 = {-6, -3}