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

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

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

Reorder the terms:
(-1 + z)(z + -2) = 0

Reorder the terms:
(-1 + z)(-2 + z) = 0

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

Combine like terms: -1z + -2z = -3z
(2 + -3z + z2) = 0

Solving
2 + -3z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Subproblem 2
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
Solution
z = {1, 2}