(5u-1)(2-u)=0

Solution for (5u-1)(2-u)=0 equation:

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

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

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

Combine like terms: 1u + 10u = 11u
(-2 + 11u + -5u2) = 0

Solving
-2 + 11u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + u)(1 + -5u) = 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 + -5u)' equal to zero and attempt to solve:

Simplifying
1 + -5u = 0

Solving
1 + -5u = 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 + -5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5u = 0 + -1
-5u = 0 + -1

Combine like terms: 0 + -1 = -1
-5u = -1

Divide each side by '-5'.
u = 0.2

Simplifying
u = 0.2
Solution
u = {2, 0.2}