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

Solution for (3-u)(4u-9)=0 equation:

Simplifying
(3 + -1u)(4u + -9) = 0

Reorder the terms:
(3 + -1u)(-9 + 4u) = 0

Multiply (3 + -1u) * (-9 + 4u)
(3(-9 + 4u) + -1u * (-9 + 4u)) = 0
((-9 * 3 + 4u * 3) + -1u * (-9 + 4u)) = 0
((-27 + 12u) + -1u * (-9 + 4u)) = 0
(-27 + 12u + (-9 * -1u + 4u * -1u)) = 0
(-27 + 12u + (9u + -4u2)) = 0

Combine like terms: 12u + 9u = 21u
(-27 + 21u + -4u2) = 0

Solving
-27 + 21u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + u)(9 + -4u) = 0

Subproblem 1
Set the factor '(-3 + u)' equal to zero and attempt to solve:

Simplifying
-3 + u = 0

Solving
-3 + u = 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 + u = 0 + 3

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

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

Simplifying
u = 3
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 = {3, 2.25}