-18=3(-z+6+2)z

Solution for -18=3(-z+6+2)z equation:

Simplifying
-18 = 3(-1z + 6 + 2) * z

Reorder the terms:
-18 = 3(6 + 2 + -1z) * z

Combine like terms: 6 + 2 = 8
-18 = 3(8 + -1z) * z

Reorder the terms for easier multiplication:
-18 = 3z(8 + -1z)
-18 = (8 * 3z + -1z * 3z)
-18 = (24z + -3z2)

Solving
-18 = 24z + -3z2

Solving for variable 'z'.

Reorder the terms:
-18 + -24z + 3z2 = 24z + -24z + -3z2 + 3z2

Combine like terms: 24z + -24z = 0
-18 + -24z + 3z2 = 0 + -3z2 + 3z2
-18 + -24z + 3z2 = -3z2 + 3z2

Combine like terms: -3z2 + 3z2 = 0
-18 + -24z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -8z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -8z + z2)' equal to zero and attempt to solve:

Simplifying
-6 + -8z + z2 = 0

Solving
-6 + -8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -8z + 6 + z2 = 0 + 6

Reorder the terms:
-6 + 6 + -8z + z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -8z + z2 = 0 + 6
-8z + z2 = 0 + 6

Combine like terms: 0 + 6 = 6
-8z + z2 = 6

The z term is -8z.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8z + 16 + z2 = 6 + 16

Reorder the terms:
16 + -8z + z2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + -8z + z2 = 22

Factor a perfect square on the left side:
(z + -4)(z + -4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(z + -4) equal to 4.69041576 and -4.69041576.

Subproblem 1
z + -4 = 4.69041576

Simplifying
z + -4 = 4.69041576

Reorder the terms:
-4 + z = 4.69041576

Solving
-4 + z = 4.69041576

Solving for variable 'z'.

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

Add '4' to each side of the equation.
-4 + 4 + z = 4.69041576 + 4

Combine like terms: -4 + 4 = 0
0 + z = 4.69041576 + 4
z = 4.69041576 + 4

Combine like terms: 4.69041576 + 4 = 8.69041576
z = 8.69041576

Simplifying
z = 8.69041576

Subproblem 2
z + -4 = -4.69041576

Simplifying
z + -4 = -4.69041576

Reorder the terms:
-4 + z = -4.69041576

Solving
-4 + z = -4.69041576

Solving for variable 'z'.

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

Add '4' to each side of the equation.
-4 + 4 + z = -4.69041576 + 4

Combine like terms: -4 + 4 = 0
0 + z = -4.69041576 + 4
z = -4.69041576 + 4

Combine like terms: -4.69041576 + 4 = -0.69041576
z = -0.69041576

Simplifying
z = -0.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {8.69041576, -0.69041576}
Solution
z = {8.69041576, -0.69041576}