(3u-1)(6-u)=0

Solution for (3u-1)(6-u)=0 equation:

Simplifying
(3u + -1)(6 + -1u) = 0

Reorder the terms:
(-1 + 3u)(6 + -1u) = 0

Multiply (-1 + 3u) * (6 + -1u)
(-1(6 + -1u) + 3u * (6 + -1u)) = 0
((6 * -1 + -1u * -1) + 3u * (6 + -1u)) = 0
((-6 + 1u) + 3u * (6 + -1u)) = 0
(-6 + 1u + (6 * 3u + -1u * 3u)) = 0
(-6 + 1u + (18u + -3u2)) = 0

Combine like terms: 1u + 18u = 19u
(-6 + 19u + -3u2) = 0

Solving
-6 + 19u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + u)(1 + -3u) = 0

Subproblem 1
Set the factor '(-6 + u)' equal to zero and attempt to solve:

Simplifying
-6 + u = 0

Solving
-6 + u = 0

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

Add '6' to each side of the equation.
-6 + 6 + u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + u = 0 + 6
u = 0 + 6

Combine like terms: 0 + 6 = 6
u = 6

Simplifying
u = 6
Subproblem 2
Set the factor '(1 + -3u)' equal to zero and attempt to solve:

Simplifying
1 + -3u = 0

Solving
1 + -3u = 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 + -3u = 0 + -1

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

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

Divide each side by '-3'.
u = 0.3333333333

Simplifying
u = 0.3333333333
Solution
u = {6, 0.3333333333}