(4u-9)(6-u)=0

Solution for (4u-9)(6-u)=0 equation:

Simplifying
(4u + -9)(6 + -1u) = 0

Reorder the terms:
(-9 + 4u)(6 + -1u) = 0

Multiply (-9 + 4u) * (6 + -1u)
(-9(6 + -1u) + 4u * (6 + -1u)) = 0
((6 * -9 + -1u * -9) + 4u * (6 + -1u)) = 0
((-54 + 9u) + 4u * (6 + -1u)) = 0
(-54 + 9u + (6 * 4u + -1u * 4u)) = 0
(-54 + 9u + (24u + -4u2)) = 0

Combine like terms: 9u + 24u = 33u
(-54 + 33u + -4u2) = 0

Solving
-54 + 33u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + u)(9 + -4u) = 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 + -4u)' equal to zero and attempt to solve:

Simplifying
9 + -4u = 0

Solving
9 + -4u = 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 + -4u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4u = 0 + -9
-4u = 0 + -9

Combine like terms: 0 + -9 = -9
-4u = -9

Divide each side by '-4'.
u = 2.25

Simplifying
u = 2.25
Solution
u = {6, 2.25}