(2z-6)(z-2)=0

Solution for (2z-6)(z-2)=0 equation:

Simplifying
(2z + -6)(z + -2) = 0

Reorder the terms:
(-6 + 2z)(z + -2) = 0

Reorder the terms:
(-6 + 2z)(-2 + z) = 0

Multiply (-6 + 2z) * (-2 + z)
(-6(-2 + z) + 2z * (-2 + z)) = 0
((-2 * -6 + z * -6) + 2z * (-2 + z)) = 0
((12 + -6z) + 2z * (-2 + z)) = 0
(12 + -6z + (-2 * 2z + z * 2z)) = 0
(12 + -6z + (-4z + 2z2)) = 0

Combine like terms: -6z + -4z = -10z
(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}