(a-1)(a-2)=0

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

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

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

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

Multiply (-1 + a) * (-2 + a)
(-1(-2 + a) + a(-2 + a)) = 0
((-2 * -1 + a * -1) + a(-2 + a)) = 0
((2 + -1a) + a(-2 + a)) = 0
(2 + -1a + (-2 * a + a * a)) = 0
(2 + -1a + (-2a + a2)) = 0

Combine like terms: -1a + -2a = -3a
(2 + -3a + a2) = 0

Solving
2 + -3a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

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

Simplifying
a = 2
Solution
a = {1, 2}