-3(u-2)(-u-1)=0

Solution for -3(u-2)(-u-1)=0 equation:

Simplifying
-3(u + -2)(-1u + -1) = 0

Reorder the terms:
-3(-2 + u)(-1u + -1) = 0

Reorder the terms:
-3(-2 + u)(-1 + -1u) = 0

Multiply (-2 + u) * (-1 + -1u)
-3(-2(-1 + -1u) + u(-1 + -1u)) = 0
-3((-1 * -2 + -1u * -2) + u(-1 + -1u)) = 0
-3((2 + 2u) + u(-1 + -1u)) = 0
-3(2 + 2u + (-1 * u + -1u * u)) = 0
-3(2 + 2u + (-1u + -1u2)) = 0

Combine like terms: 2u + -1u = 1u
-3(2 + 1u + -1u2) = 0
(2 * -3 + 1u * -3 + -1u2 * -3) = 0
(-6 + -3u + 3u2) = 0

Solving
-6 + -3u + 3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1u + u2) = 0

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

Ignore the factor 3.
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}