2(3z-2)*(2z)=66

Solution for 2(3z-2)*(2z)=66 equation:

Simplifying
2(3z + -2)(2z) = 66

Reorder the terms:
2(-2 + 3z)(2z) = 66

Remove parenthesis around (2z)
2(-2 + 3z) * 2z = 66

Reorder the terms for easier multiplication:
2 * 2z(-2 + 3z) = 66

Multiply 2 * 2
4z(-2 + 3z) = 66
(-2 * 4z + 3z * 4z) = 66
(-8z + 12z2) = 66

Solving
-8z + 12z2 = 66

Solving for variable 'z'.

Reorder the terms:
-66 + -8z + 12z2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -8z + 12z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -4z + 6z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-33 + -4z + 6z2)' equal to zero and attempt to solve:

Simplifying
-33 + -4z + 6z2 = 0

Solving
-33 + -4z + 6z2 = 0

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

Divide each side by '6'.
-5.5 + -0.6666666667z + z2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -0.6666666667z + 5.5 + z2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -0.6666666667z + z2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -0.6666666667z + z2 = 0 + 5.5
-0.6666666667z + z2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-0.6666666667z + z2 = 5.5

The z term is -0.6666666667z.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667z + 0.1111111112 + z2 = 5.5 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667z + z2 = 5.5 + 0.1111111112

Combine like terms: 5.5 + 0.1111111112 = 5.6111111112
0.1111111112 + -0.6666666667z + z2 = 5.6111111112

Factor a perfect square on the left side:
(z + -0.3333333334)(z + -0.3333333334) = 5.6111111112

Calculate the square root of the right side: 2.368778401

Break this problem into two subproblems by setting 
(z + -0.3333333334) equal to 2.368778401 and -2.368778401.

Subproblem 1
z + -0.3333333334 = 2.368778401

Simplifying
z + -0.3333333334 = 2.368778401

Reorder the terms:
-0.3333333334 + z = 2.368778401

Solving
-0.3333333334 + z = 2.368778401

Solving for variable 'z'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + z = 2.368778401 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + z = 2.368778401 + 0.3333333334
z = 2.368778401 + 0.3333333334

Combine like terms: 2.368778401 + 0.3333333334 = 2.7021117344
z = 2.7021117344

Simplifying
z = 2.7021117344

Subproblem 2
z + -0.3333333334 = -2.368778401

Simplifying
z + -0.3333333334 = -2.368778401

Reorder the terms:
-0.3333333334 + z = -2.368778401

Solving
-0.3333333334 + z = -2.368778401

Solving for variable 'z'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + z = -2.368778401 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + z = -2.368778401 + 0.3333333334
z = -2.368778401 + 0.3333333334

Combine like terms: -2.368778401 + 0.3333333334 = -2.0354450676
z = -2.0354450676

Simplifying
z = -2.0354450676

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.7021117344, -2.0354450676}
Solution
z = {2.7021117344, -2.0354450676}