9(y+3)(y+6)=

Solution for 9(y+3)(y+6)= equation:

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

Reorder the terms:
9(3 + y)(y + 6) = 0

Reorder the terms:
9(3 + y)(6 + y) = 0

Multiply (3 + y) * (6 + y)
9(3(6 + y) + y(6 + y)) = 0
9((6 * 3 + y * 3) + y(6 + y)) = 0
9((18 + 3y) + y(6 + y)) = 0
9(18 + 3y + (6 * y + y * y)) = 0
9(18 + 3y + (6y + y2)) = 0

Combine like terms: 3y + 6y = 9y
9(18 + 9y + y2) = 0
(18 * 9 + 9y * 9 + y2 * 9) = 0
(162 + 81y + 9y2) = 0

Solving
162 + 81y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9'.
9(18 + 9y + y2) = 0

Factor a trinomial.
9((6 + y)(3 + y)) = 0

Ignore the factor 9.
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}