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

Solution for (6+u)(3u+4)=0 equation:

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

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

Multiply (6 + u) * (4 + 3u)
(6(4 + 3u) + u(4 + 3u)) = 0
((4 * 6 + 3u * 6) + u(4 + 3u)) = 0
((24 + 18u) + u(4 + 3u)) = 0
(24 + 18u + (4 * u + 3u * u)) = 0
(24 + 18u + (4u + 3u2)) = 0

Combine like terms: 18u + 4u = 22u
(24 + 22u + 3u2) = 0

Solving
24 + 22u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(4 + 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 '(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 = {-6, -1.333333333}