z^2+18z+72=0

Solution for z^2+18z+72=0 equation:

Simplifying
z2 + 18z + 72 = 0

Reorder the terms:
72 + 18z + z2 = 0

Solving
72 + 18z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(12 + z)(6 + z) = 0

Subproblem 1
Set the factor '(12 + z)' equal to zero and attempt to solve:

Simplifying
12 + z = 0

Solving
12 + z = 0

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

Add '-12' to each side of the equation.
12 + -12 + z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + z = 0 + -12
z = 0 + -12

Combine like terms: 0 + -12 = -12
z = -12

Simplifying
z = -12
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 = {-12, -6}