(3u+4)(9+u)=0

Solution for (3u+4)(9+u)=0 equation:

Simplifying
(3u + 4)(9 + u) = 0

Reorder the terms:
(4 + 3u)(9 + u) = 0

Multiply (4 + 3u) * (9 + u)
(4(9 + u) + 3u * (9 + u)) = 0
((9 * 4 + u * 4) + 3u * (9 + u)) = 0
((36 + 4u) + 3u * (9 + u)) = 0
(36 + 4u + (9 * 3u + u * 3u)) = 0
(36 + 4u + (27u + 3u2)) = 0

Combine like terms: 4u + 27u = 31u
(36 + 31u + 3u2) = 0

Solving
36 + 31u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(9 + u)(4 + 3u) = 0

Subproblem 1
Set the factor '(9 + u)' equal to zero and attempt to solve:

Simplifying
9 + u = 0

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

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

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

Simplifying
u = -9
Subproblem 2
Set the factor '(4 + 3u)' equal to zero and attempt to solve:

Simplifying
4 + 3u = 0

Solving
4 + 3u = 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 + 3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3u = 0 + -4
3u = 0 + -4

Combine like terms: 0 + -4 = -4
3u = -4

Divide each side by '3'.
u = -1.333333333

Simplifying
u = -1.333333333
Solution
u = {-9, -1.333333333}