(5u-8)(1-u)=0

Solution for (5u-8)(1-u)=0 equation:

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

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

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

Combine like terms: 8u + 5u = 13u
(-8 + 13u + -5u2) = 0

Solving
-8 + 13u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-8 + 5u)(1 + -1u) = 0

Subproblem 1
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
Subproblem 2
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
Solution
u = {1.6, 1}