(z^2)-(6z)-(27)=0

Solution for (z^2)-(6z)-(27)=0 equation:

Simplifying
(z2) + -1(6z) + -1(27) = 0
z2 + -1(6z) + -1(27) = 0

Remove parenthesis around (6z)
z2 + -1 * 6z + -1(27) = 0

Multiply -1 * 6
z2 + -6z + -1(27) = 0

Multiply -1 * 27
z2 + -6z + -27 = 0

Reorder the terms:
-27 + -6z + z2 = 0

Solving
-27 + -6z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 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 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

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