(u-2)(u-1)=0

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

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

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

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

Multiply (-2 + u) * (-1 + u)
(-2(-1 + u) + u(-1 + u)) = 0
((-1 * -2 + u * -2) + u(-1 + u)) = 0
((2 + -2u) + u(-1 + u)) = 0
(2 + -2u + (-1 * u + u * u)) = 0
(2 + -2u + (-1u + u2)) = 0

Combine like terms: -2u + -1u = -3u
(2 + -3u + u2) = 0

Solving
2 + -3u + u2 = 0

Solving for variable 'u'.

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

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

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

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

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

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