(2u+9)(4+u)=0

Solution for (2u+9)(4+u)=0 equation:

Simplifying
(2u + 9)(4 + u) = 0

Reorder the terms:
(9 + 2u)(4 + u) = 0

Multiply (9 + 2u) * (4 + u)
(9(4 + u) + 2u * (4 + u)) = 0
((4 * 9 + u * 9) + 2u * (4 + u)) = 0
((36 + 9u) + 2u * (4 + u)) = 0
(36 + 9u + (4 * 2u + u * 2u)) = 0
(36 + 9u + (8u + 2u2)) = 0

Combine like terms: 9u + 8u = 17u
(36 + 17u + 2u2) = 0

Solving
36 + 17u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(9 + 2u)(4 + u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4
Solution
u = {-4.5, -4}