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

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

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

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

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

Multiply 3 * 2
-18 = 6z(6 + -1z)
-18 = (6 * 6z + -1z * 6z)
-18 = (36z + -6z2)

Solving
-18 = 36z + -6z2

Solving for variable 'z'.

Reorder the terms:
-18 + -36z + 6z2 = 36z + -36z + -6z2 + 6z2

Combine like terms: 36z + -36z = 0
-18 + -36z + 6z2 = 0 + -6z2 + 6z2
-18 + -36z + 6z2 = -6z2 + 6z2

Combine like terms: -6z2 + 6z2 = 0
-18 + -36z + 6z2 = 0

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

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

Simplifying
-3 + -6z + z2 = 0

Solving
-3 + -6z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + -6z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6z + z2 = 0 + 3
-6z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6z + z2 = 3

The z term is -6z.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6z + 9 + z2 = 3 + 9

Reorder the terms:
9 + -6z + z2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + -6z + z2 = 12

Factor a perfect square on the left side:
(z + -3)(z + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1
z + -3 = 3.464101615

Simplifying
z + -3 = 3.464101615

Reorder the terms:
-3 + z = 3.464101615

Solving
-3 + z = 3.464101615

Solving for variable 'z'.

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

Add '3' to each side of the equation.
-3 + 3 + z = 3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + z = 3.464101615 + 3
z = 3.464101615 + 3

Combine like terms: 3.464101615 + 3 = 6.464101615
z = 6.464101615

Simplifying
z = 6.464101615

Subproblem 2
z + -3 = -3.464101615

Simplifying
z + -3 = -3.464101615

Reorder the terms:
-3 + z = -3.464101615

Solving
-3 + z = -3.464101615

Solving for variable 'z'.

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

Add '3' to each side of the equation.
-3 + 3 + z = -3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + z = -3.464101615 + 3
z = -3.464101615 + 3

Combine like terms: -3.464101615 + 3 = -0.464101615
z = -0.464101615

Simplifying
z = -0.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {6.464101615, -0.464101615}
Solution
z = {6.464101615, -0.464101615}