(5u+9)(6-u)=0

Solution for (5u+9)(6-u)=0 equation:

Simplifying
(5u + 9)(6 + -1u) = 0

Reorder the terms:
(9 + 5u)(6 + -1u) = 0

Multiply (9 + 5u) * (6 + -1u)
(9(6 + -1u) + 5u * (6 + -1u)) = 0
((6 * 9 + -1u * 9) + 5u * (6 + -1u)) = 0
((54 + -9u) + 5u * (6 + -1u)) = 0
(54 + -9u + (6 * 5u + -1u * 5u)) = 0
(54 + -9u + (30u + -5u2)) = 0

Combine like terms: -9u + 30u = 21u
(54 + 21u + -5u2) = 0

Solving
54 + 21u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(9 + 5u) = 0

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

Simplifying
6 + -1u = 0

Solving
6 + -1u = 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 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Subproblem 2
Set the factor '(9 + 5u)' equal to zero and attempt to solve:

Simplifying
9 + 5u = 0

Solving
9 + 5u = 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 + 5u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5u = 0 + -9
5u = 0 + -9

Combine like terms: 0 + -9 = -9
5u = -9

Divide each side by '5'.
u = -1.8

Simplifying
u = -1.8
Solution
u = {6, -1.8}