(3-u)(5u-8)=0

Solution for (3-u)(5u-8)=0 equation:

Simplifying
(3 + -1u)(5u + -8) = 0

Reorder the terms:
(3 + -1u)(-8 + 5u) = 0

Multiply (3 + -1u) * (-8 + 5u)
(3(-8 + 5u) + -1u * (-8 + 5u)) = 0
((-8 * 3 + 5u * 3) + -1u * (-8 + 5u)) = 0
((-24 + 15u) + -1u * (-8 + 5u)) = 0
(-24 + 15u + (-8 * -1u + 5u * -1u)) = 0
(-24 + 15u + (8u + -5u2)) = 0

Combine like terms: 15u + 8u = 23u
(-24 + 23u + -5u2) = 0

Solving
-24 + 23u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + u)(8 + -5u) = 0

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

Simplifying
-3 + u = 0

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

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

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

Simplifying
u = 3
Subproblem 2
Set the factor '(8 + -5u)' equal to zero and attempt to solve:

Simplifying
8 + -5u = 0

Solving
8 + -5u = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5u = 0 + -8
-5u = 0 + -8

Combine like terms: 0 + -8 = -8
-5u = -8

Divide each side by '-5'.
u = 1.6

Simplifying
u = 1.6
Solution
u = {3, 1.6}