(4u+9)(6+u)=0

Solution for (4u+9)(6+u)=0 equation:

Simplifying
(4u + 9)(6 + u) = 0

Reorder the terms:
(9 + 4u)(6 + u) = 0

Multiply (9 + 4u) * (6 + u)
(9(6 + u) + 4u * (6 + u)) = 0
((6 * 9 + u * 9) + 4u * (6 + u)) = 0
((54 + 9u) + 4u * (6 + u)) = 0
(54 + 9u + (6 * 4u + u * 4u)) = 0
(54 + 9u + (24u + 4u2)) = 0

Combine like terms: 9u + 24u = 33u
(54 + 33u + 4u2) = 0

Solving
54 + 33u + 4u2 = 0

Solving for variable 'u'.

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

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

Simplifying
6 + u = 0

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

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

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

Simplifying
u = -6
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 = {-6, -2.25}