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

Solution for (3-u)(2u-9)=0 equation:

Simplifying
(3 + -1u)(2u + -9) = 0

Reorder the terms:
(3 + -1u)(-9 + 2u) = 0

Multiply (3 + -1u) * (-9 + 2u)
(3(-9 + 2u) + -1u * (-9 + 2u)) = 0
((-9 * 3 + 2u * 3) + -1u * (-9 + 2u)) = 0
((-27 + 6u) + -1u * (-9 + 2u)) = 0
(-27 + 6u + (-9 * -1u + 2u * -1u)) = 0
(-27 + 6u + (9u + -2u2)) = 0

Combine like terms: 6u + 9u = 15u
(-27 + 15u + -2u2) = 0

Solving
-27 + 15u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + 2u)(3 + -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 '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {4.5, 3}