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

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

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

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

Multiply (6 + 5u) * (9 + -1u)
(6(9 + -1u) + 5u * (9 + -1u)) = 0
((9 * 6 + -1u * 6) + 5u * (9 + -1u)) = 0
((54 + -6u) + 5u * (9 + -1u)) = 0
(54 + -6u + (9 * 5u + -1u * 5u)) = 0
(54 + -6u + (45u + -5u2)) = 0

Combine like terms: -6u + 45u = 39u
(54 + 39u + -5u2) = 0

Solving
54 + 39u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(9 + -1u)(6 + 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 '(6 + 5u)' equal to zero and attempt to solve:

Simplifying
6 + 5u = 0

Solving
6 + 5u = 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 + 5u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5u = 0 + -6
5u = 0 + -6

Combine like terms: 0 + -6 = -6
5u = -6

Divide each side by '5'.
u = -1.2

Simplifying
u = -1.2
Solution
u = {9, -1.2}