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

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

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

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

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

Combine like terms: -9u + 6u = -3u
(27 + -3u + -2u2) = 0

Solving
27 + -3u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + -1u)(9 + 2u) = 0

Subproblem 1
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
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 = {3, -4.5}