(3u+7)(9+u)=0

Solution for (3u+7)(9+u)=0 equation:

Simplifying
(3u + 7)(9 + u) = 0

Reorder the terms:
(7 + 3u)(9 + u) = 0

Multiply (7 + 3u) * (9 + u)
(7(9 + u) + 3u * (9 + u)) = 0
((9 * 7 + u * 7) + 3u * (9 + u)) = 0
((63 + 7u) + 3u * (9 + u)) = 0
(63 + 7u + (9 * 3u + u * 3u)) = 0
(63 + 7u + (27u + 3u2)) = 0

Combine like terms: 7u + 27u = 34u
(63 + 34u + 3u2) = 0

Solving
63 + 34u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(9 + u)(7 + 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 '(7 + 3u)' equal to zero and attempt to solve:

Simplifying
7 + 3u = 0

Solving
7 + 3u = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3u = 0 + -7
3u = 0 + -7

Combine like terms: 0 + -7 = -7
3u = -7

Divide each side by '3'.
u = -2.333333333

Simplifying
u = -2.333333333
Solution
u = {-9, -2.333333333}