(z+3)(z+9)=0

Solution for (z+3)(z+9)=0 equation:

Simplifying
(z + 3)(z + 9) = 0

Reorder the terms:
(3 + z)(z + 9) = 0

Reorder the terms:
(3 + z)(9 + z) = 0

Multiply (3 + z) * (9 + z)
(3(9 + z) + z(9 + z)) = 0
((9 * 3 + z * 3) + z(9 + z)) = 0
((27 + 3z) + z(9 + z)) = 0
(27 + 3z + (9 * z + z * z)) = 0
(27 + 3z + (9z + z2)) = 0

Combine like terms: 3z + 9z = 12z
(27 + 12z + z2) = 0

Solving
27 + 12z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + z)(3 + z) = 0

Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 0

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

Add '-9' to each side of the equation.
9 + -9 + z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + z = 0 + -9
z = 0 + -9

Combine like terms: 0 + -9 = -9
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-9, -3}