z^2+18z+45=0

Solution for z^2+18z+45=0 equation:

Simplifying
z2 + 18z + 45 = 0

Reorder the terms:
45 + 18z + z2 = 0

Solving
45 + 18z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(15 + z)' equal to zero and attempt to solve:

Simplifying
15 + z = 0

Solving
15 + z = 0

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

Add '-15' to each side of the equation.
15 + -15 + z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + z = 0 + -15
z = 0 + -15

Combine like terms: 0 + -15 = -15
z = -15

Simplifying
z = -15
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 = {-15, -3}