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

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

Simplifying
(4u + 3)(6 + -1u) = 0

Reorder the terms:
(3 + 4u)(6 + -1u) = 0

Multiply (3 + 4u) * (6 + -1u)
(3(6 + -1u) + 4u * (6 + -1u)) = 0
((6 * 3 + -1u * 3) + 4u * (6 + -1u)) = 0
((18 + -3u) + 4u * (6 + -1u)) = 0
(18 + -3u + (6 * 4u + -1u * 4u)) = 0
(18 + -3u + (24u + -4u2)) = 0

Combine like terms: -3u + 24u = 21u
(18 + 21u + -4u2) = 0

Solving
18 + 21u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(3 + 4u) = 0

Subproblem 1
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 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 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
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}