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

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

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

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

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

Combine like terms: 3u + 24u = 27u
(18 + 27u + 4u2) = 0

Solving
18 + 27u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(3 + 4u) = 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 '(3 + 4u)' equal to zero and attempt to solve:

Simplifying
3 + 4u = 0

Solving
3 + 4u = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4u = 0 + -3

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

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

Divide each side by '4'.
u = -0.75

Simplifying
u = -0.75
Solution
u = {-6, -0.75}