(z^2)+(15z)+(54)=0

Solution for (z^2)+(15z)+(54)=0 equation:

Simplifying
(z2) + (15z) + (54) = 0
z2 + (15z) + (54) = 0
z2 + (15z) + 54 = 0

Reorder the terms:
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}