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

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

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

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

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

Combine like terms: 8u + 1u = 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}