(1-u)(5u-9)=0

Solution for (1-u)(5u-9)=0 equation:

Simplifying
(1 + -1u)(5u + -9) = 0

Reorder the terms:
(1 + -1u)(-9 + 5u) = 0

Multiply (1 + -1u) * (-9 + 5u)
(1(-9 + 5u) + -1u * (-9 + 5u)) = 0
((-9 * 1 + 5u * 1) + -1u * (-9 + 5u)) = 0
((-9 + 5u) + -1u * (-9 + 5u)) = 0
(-9 + 5u + (-9 * -1u + 5u * -1u)) = 0
(-9 + 5u + (9u + -5u2)) = 0

Combine like terms: 5u + 9u = 14u
(-9 + 14u + -5u2) = 0

Solving
-9 + 14u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + 5u)(1 + -1u) = 0

Subproblem 1
Set the factor '(-9 + 5u)' equal to zero and attempt to solve:

Simplifying
-9 + 5u = 0

Solving
-9 + 5u = 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 + 5u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5u = 0 + 9
5u = 0 + 9

Combine like terms: 0 + 9 = 9
5u = 9

Divide each side by '5'.
u = 1.8

Simplifying
u = 1.8
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 = {1.8, 1}