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

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

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

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

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

Combine like terms: 9u + 2u = 11u
(-9 + 11u + -2u2) = 0

Solving
-9 + 11u + -2u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(-9 + 2u)' equal to zero and attempt to solve:

Simplifying
-9 + 2u = 0

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

Combine like terms: -9 + 9 = 0
0 + 2u = 0 + 9
2u = 0 + 9

Combine like terms: 0 + 9 = 9
2u = 9

Divide each side by '2'.
u = 4.5

Simplifying
u = 4.5
Subproblem 2
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

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

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

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

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Solution
u = {4.5, 1}