(u-2)(u-3)=0

Solution for (u-2)(u-3)=0 equation:

Simplifying
(u + -2)(u + -3) = 0

Reorder the terms:
(-2 + u)(u + -3) = 0

Reorder the terms:
(-2 + u)(-3 + u) = 0

Multiply (-2 + u) * (-3 + u)
(-2(-3 + u) + u(-3 + u)) = 0
((-3 * -2 + u * -2) + u(-3 + u)) = 0
((6 + -2u) + u(-3 + u)) = 0
(6 + -2u + (-3 * u + u * u)) = 0
(6 + -2u + (-3u + u2)) = 0

Combine like terms: -2u + -3u = -5u
(6 + -5u + u2) = 0

Solving
6 + -5u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + -1u)(3 + -1u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {2, 3}