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

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

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

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

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

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

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

Solving for variable 'u'.

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

Simplifying
1 + -4u = 0

Solving
1 + -4u = 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 + -4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4u = 0 + -1
-4u = 0 + -1

Combine like terms: 0 + -1 = -1
-4u = -1

Divide each side by '-4'.
u = 0.25

Simplifying
u = 0.25
Solution
u = {2, 0.25}