2z^2+18z-330=0

Solution for 2z^2+18z-330=0 equation:

Simplifying
2z2 + 18z + -330 = 0

Reorder the terms:
-330 + 18z + 2z2 = 0

Solving
-330 + 18z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-165 + 9z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-165 + 9z + z2)' equal to zero and attempt to solve:

Simplifying
-165 + 9z + z2 = 0

Solving
-165 + 9z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + 9z + 165 + z2 = 0 + 165

Reorder the terms:
-165 + 165 + 9z + z2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + 9z + z2 = 0 + 165
9z + z2 = 0 + 165

Combine like terms: 0 + 165 = 165
9z + z2 = 165

The z term is 9z.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9z + 20.25 + z2 = 165 + 20.25

Reorder the terms:
20.25 + 9z + z2 = 165 + 20.25

Combine like terms: 165 + 20.25 = 185.25
20.25 + 9z + z2 = 185.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 185.25

Calculate the square root of the right side: 13.610657589

Break this problem into two subproblems by setting 
(z + 4.5) equal to 13.610657589 and -13.610657589.

Subproblem 1
z + 4.5 = 13.610657589

Simplifying
z + 4.5 = 13.610657589

Reorder the terms:
4.5 + z = 13.610657589

Solving
4.5 + z = 13.610657589

Solving for variable 'z'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + z = 13.610657589 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = 13.610657589 + -4.5
z = 13.610657589 + -4.5

Combine like terms: 13.610657589 + -4.5 = 9.110657589
z = 9.110657589

Simplifying
z = 9.110657589

Subproblem 2
z + 4.5 = -13.610657589

Simplifying
z + 4.5 = -13.610657589

Reorder the terms:
4.5 + z = -13.610657589

Solving
4.5 + z = -13.610657589

Solving for variable 'z'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + z = -13.610657589 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = -13.610657589 + -4.5
z = -13.610657589 + -4.5

Combine like terms: -13.610657589 + -4.5 = -18.110657589
z = -18.110657589

Simplifying
z = -18.110657589

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {9.110657589, -18.110657589}
Solution
z = {9.110657589, -18.110657589}