(5u+3)(9-u)=0

Solution for (5u+3)(9-u)=0 equation:

Simplifying
(5u + 3)(9 + -1u) = 0

Reorder the terms:
(3 + 5u)(9 + -1u) = 0

Multiply (3 + 5u) * (9 + -1u)
(3(9 + -1u) + 5u * (9 + -1u)) = 0
((9 * 3 + -1u * 3) + 5u * (9 + -1u)) = 0
((27 + -3u) + 5u * (9 + -1u)) = 0
(27 + -3u + (9 * 5u + -1u * 5u)) = 0
(27 + -3u + (45u + -5u2)) = 0

Combine like terms: -3u + 45u = 42u
(27 + 42u + -5u2) = 0

Solving
27 + 42u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(9 + -1u)(3 + 5u) = 0

Subproblem 1
Set the factor '(9 + -1u)' equal to zero and attempt to solve:

Simplifying
9 + -1u = 0

Solving
9 + -1u = 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 + -1u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1u = 0 + -9
-1u = 0 + -9

Combine like terms: 0 + -9 = -9
-1u = -9

Divide each side by '-1'.
u = 9

Simplifying
u = 9
Subproblem 2
Set the factor '(3 + 5u)' equal to zero and attempt to solve:

Simplifying
3 + 5u = 0

Solving
3 + 5u = 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 + 5u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5u = 0 + -3
5u = 0 + -3

Combine like terms: 0 + -3 = -3
5u = -3

Divide each side by '5'.
u = -0.6

Simplifying
u = -0.6
Solution
u = {9, -0.6}