(3u-5)(6-u)=0

Solution for (3u-5)(6-u)=0 equation:

Simplifying
(3u + -5)(6 + -1u) = 0

Reorder the terms:
(-5 + 3u)(6 + -1u) = 0

Multiply (-5 + 3u) * (6 + -1u)
(-5(6 + -1u) + 3u * (6 + -1u)) = 0
((6 * -5 + -1u * -5) + 3u * (6 + -1u)) = 0
((-30 + 5u) + 3u * (6 + -1u)) = 0
(-30 + 5u + (6 * 3u + -1u * 3u)) = 0
(-30 + 5u + (18u + -3u2)) = 0

Combine like terms: 5u + 18u = 23u
(-30 + 23u + -3u2) = 0

Solving
-30 + 23u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + u)(5 + -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 '(5 + -3u)' equal to zero and attempt to solve:

Simplifying
5 + -3u = 0

Solving
5 + -3u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3u = 0 + -5
-3u = 0 + -5

Combine like terms: 0 + -5 = -5
-3u = -5

Divide each side by '-3'.
u = 1.666666667

Simplifying
u = 1.666666667
Solution
u = {6, 1.666666667}