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

Solution for (6-u)(2u-9)=0 equation:

Simplifying
(6 + -1u)(2u + -9) = 0

Reorder the terms:
(6 + -1u)(-9 + 2u) = 0

Multiply (6 + -1u) * (-9 + 2u)
(6(-9 + 2u) + -1u * (-9 + 2u)) = 0
((-9 * 6 + 2u * 6) + -1u * (-9 + 2u)) = 0
((-54 + 12u) + -1u * (-9 + 2u)) = 0
(-54 + 12u + (-9 * -1u + 2u * -1u)) = 0
(-54 + 12u + (9u + -2u2)) = 0

Combine like terms: 12u + 9u = 21u
(-54 + 21u + -2u2) = 0

Solving
-54 + 21u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + u)(9 + -2u) = 0

Subproblem 1
Set the factor '(-6 + u)' equal to zero and attempt to solve:

Simplifying
-6 + u = 0

Solving
-6 + u = 0

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

Add '6' to each side of the equation.
-6 + 6 + u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + u = 0 + 6
u = 0 + 6

Combine like terms: 0 + 6 = 6
u = 6

Simplifying
u = 6
Subproblem 2
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
Solution
u = {6, 4.5}