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

Solution for (6+u)(3u+7)=0 equation:

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

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

Multiply (6 + u) * (7 + 3u)
(6(7 + 3u) + u(7 + 3u)) = 0
((7 * 6 + 3u * 6) + u(7 + 3u)) = 0
((42 + 18u) + u(7 + 3u)) = 0
(42 + 18u + (7 * u + 3u * u)) = 0
(42 + 18u + (7u + 3u2)) = 0

Combine like terms: 18u + 7u = 25u
(42 + 25u + 3u2) = 0

Solving
42 + 25u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(7 + 3u) = 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 '(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 = {-6, -2.333333333}