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

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

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

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

Multiply (-5 + 4u) * (4 + -1u)
(-5(4 + -1u) + 4u * (4 + -1u)) = 0
((4 * -5 + -1u * -5) + 4u * (4 + -1u)) = 0
((-20 + 5u) + 4u * (4 + -1u)) = 0
(-20 + 5u + (4 * 4u + -1u * 4u)) = 0
(-20 + 5u + (16u + -4u2)) = 0

Combine like terms: 5u + 16u = 21u
(-20 + 21u + -4u2) = 0

Solving
-20 + 21u + -4u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(-4 + u)' equal to zero and attempt to solve:

Simplifying
-4 + u = 0

Solving
-4 + u = 0

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

Add '4' to each side of the equation.
-4 + 4 + u = 0 + 4

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

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

Simplifying
u = 4
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 = {4, 1.25}