(2u-1)(9-u)=0

Solution for (2u-1)(9-u)=0 equation:

Simplifying
(2u + -1)(9 + -1u) = 0

Reorder the terms:
(-1 + 2u)(9 + -1u) = 0

Multiply (-1 + 2u) * (9 + -1u)
(-1(9 + -1u) + 2u * (9 + -1u)) = 0
((9 * -1 + -1u * -1) + 2u * (9 + -1u)) = 0
((-9 + 1u) + 2u * (9 + -1u)) = 0
(-9 + 1u + (9 * 2u + -1u * 2u)) = 0
(-9 + 1u + (18u + -2u2)) = 0

Combine like terms: 1u + 18u = 19u
(-9 + 19u + -2u2) = 0

Solving
-9 + 19u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + u)(1 + -2u) = 0

Subproblem 1
Set the factor '(-9 + u)' equal to zero and attempt to solve:

Simplifying
-9 + u = 0

Solving
-9 + u = 0

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

Add '9' to each side of the equation.
-9 + 9 + u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + u = 0 + 9
u = 0 + 9

Combine like terms: 0 + 9 = 9
u = 9

Simplifying
u = 9
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 = {9, 0.5}