(2u-1)(4-u)=0

Solution for (2u-1)(4-u)=0 equation:

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

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

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

Combine like terms: 1u + 8u = 9u
(-4 + 9u + -2u2) = 0

Solving
-4 + 9u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + u)(1 + -2u) = 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 '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2u = 0 + -1
-2u = 0 + -1

Combine like terms: 0 + -1 = -1
-2u = -1

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {4, 0.5}