(4u-5)(2-u)=0

Solution for (4u-5)(2-u)=0 equation:

Simplifying
(4u + -5)(2 + -1u) = 0

Reorder the terms:
(-5 + 4u)(2 + -1u) = 0

Multiply (-5 + 4u) * (2 + -1u)
(-5(2 + -1u) + 4u * (2 + -1u)) = 0
((2 * -5 + -1u * -5) + 4u * (2 + -1u)) = 0
((-10 + 5u) + 4u * (2 + -1u)) = 0
(-10 + 5u + (2 * 4u + -1u * 4u)) = 0
(-10 + 5u + (8u + -4u2)) = 0

Combine like terms: 5u + 8u = 13u
(-10 + 13u + -4u2) = 0

Solving
-10 + 13u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + u)(5 + -4u) = 0

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

Simplifying
-2 + u = 0

Solving
-2 + u = 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 + u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + u = 0 + 2
u = 0 + 2

Combine like terms: 0 + 2 = 2
u = 2

Simplifying
u = 2
Subproblem 2
Set the factor '(5 + -4u)' equal to zero and attempt to solve:

Simplifying
5 + -4u = 0

Solving
5 + -4u = 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 + -4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4u = 0 + -5
-4u = 0 + -5

Combine like terms: 0 + -5 = -5
-4u = -5

Divide each side by '-4'.
u = 1.25

Simplifying
u = 1.25
Solution
u = {2, 1.25}