(y-2)(y-1)=0

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

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

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

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

Multiply (-2 + y) * (-1 + y)
(-2(-1 + y) + y(-1 + y)) = 0
((-1 * -2 + y * -2) + y(-1 + y)) = 0
((2 + -2y) + y(-1 + y)) = 0
(2 + -2y + (-1 * y + y * y)) = 0
(2 + -2y + (-1y + y2)) = 0

Combine like terms: -2y + -1y = -3y
(2 + -3y + y2) = 0

Solving
2 + -3y + y2 = 0

Solving for variable 'y'.

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

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

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