2((2+-1z)(3+-1z))=0

Solution for 2((2+-1z)(3+-1z))=0 equation:

Simplifying
2((2 + -1z)(3 + -1z)) = 0

Multiply (2 + -1z) * (3 + -1z)
2((2(3 + -1z) + -1z * (3 + -1z))) = 0
2(((3 * 2 + -1z * 2) + -1z * (3 + -1z))) = 0
2(((6 + -2z) + -1z * (3 + -1z))) = 0
2((6 + -2z + (3 * -1z + -1z * -1z))) = 0
2((6 + -2z + (-3z + 1z2))) = 0

Combine like terms: -2z + -3z = -5z
2((6 + -5z + 1z2)) = 0
(6 * 2 + -5z * 2 + 1z2 * 2) = 0
(12 + -10z + 2z2) = 0

Solving
12 + -10z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5z + z2) = 0

Factor a trinomial.
2((2 + -1z)(3 + -1z)) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {2, 3}