9z^2+18z-48=0

Solution for 9z^2+18z-48=0 equation:

Simplifying
9z2 + 18z + -48 = 0

Reorder the terms:
-48 + 18z + 9z2 = 0

Solving
-48 + 18z + 9z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 6z + 3z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-16 + 6z + 3z2)' equal to zero and attempt to solve:

Simplifying
-16 + 6z + 3z2 = 0

Solving
-16 + 6z + 3z2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-5.333333333 + 2z + z2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 2z + 5.333333333 + z2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 2z + z2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 2z + z2 = 0 + 5.333333333
2z + z2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
2z + z2 = 5.333333333

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = 5.333333333 + 1

Reorder the terms:
1 + 2z + z2 = 5.333333333 + 1

Combine like terms: 5.333333333 + 1 = 6.333333333
1 + 2z + z2 = 6.333333333

Factor a perfect square on the left side:
(z + 1)(z + 1) = 6.333333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(z + 1) equal to 2.516611478 and -2.516611478.

Subproblem 1
z + 1 = 2.516611478

Simplifying
z + 1 = 2.516611478

Reorder the terms:
1 + z = 2.516611478

Solving
1 + z = 2.516611478

Solving for variable 'z'.

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

Add '-1' to each side of the equation.
1 + -1 + z = 2.516611478 + -1

Combine like terms: 1 + -1 = 0
0 + z = 2.516611478 + -1
z = 2.516611478 + -1

Combine like terms: 2.516611478 + -1 = 1.516611478
z = 1.516611478

Simplifying
z = 1.516611478

Subproblem 2
z + 1 = -2.516611478

Simplifying
z + 1 = -2.516611478

Reorder the terms:
1 + z = -2.516611478

Solving
1 + z = -2.516611478

Solving for variable 'z'.

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

Add '-1' to each side of the equation.
1 + -1 + z = -2.516611478 + -1

Combine like terms: 1 + -1 = 0
0 + z = -2.516611478 + -1
z = -2.516611478 + -1

Combine like terms: -2.516611478 + -1 = -3.516611478
z = -3.516611478

Simplifying
z = -3.516611478

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.516611478, -3.516611478}
Solution
z = {1.516611478, -3.516611478}