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

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

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

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

Multiply (9 + 4u) * (2 + u)
(9(2 + u) + 4u * (2 + u)) = 0
((2 * 9 + u * 9) + 4u * (2 + u)) = 0
((18 + 9u) + 4u * (2 + u)) = 0
(18 + 9u + (2 * 4u + u * 4u)) = 0
(18 + 9u + (8u + 4u2)) = 0

Combine like terms: 9u + 8u = 17u
(18 + 17u + 4u2) = 0

Solving
18 + 17u + 4u2 = 0

Solving for variable 'u'.

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

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

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {-2.25, -2}