(z+6)(z+9)=0

Solution for (z+6)(z+9)=0 equation:

Simplifying
(z + 6)(z + 9) = 0

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

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

Multiply (6 + z) * (9 + z)
(6(9 + z) + z(9 + z)) = 0
((9 * 6 + z * 6) + z(9 + z)) = 0
((54 + 6z) + z(9 + z)) = 0
(54 + 6z + (9 * z + z * z)) = 0
(54 + 6z + (9z + z2)) = 0

Combine like terms: 6z + 9z = 15z
(54 + 15z + z2) = 0

Solving
54 + 15z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + z)(6 + 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 '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Solution
z = {-9, -6}