(2u+3)(4-u)=0

Solution for (2u+3)(4-u)=0 equation:

Simplifying
(2u + 3)(4 + -1u) = 0

Reorder the terms:
(3 + 2u)(4 + -1u) = 0

Multiply (3 + 2u) * (4 + -1u)
(3(4 + -1u) + 2u * (4 + -1u)) = 0
((4 * 3 + -1u * 3) + 2u * (4 + -1u)) = 0
((12 + -3u) + 2u * (4 + -1u)) = 0
(12 + -3u + (4 * 2u + -1u * 2u)) = 0
(12 + -3u + (8u + -2u2)) = 0

Combine like terms: -3u + 8u = 5u
(12 + 5u + -2u2) = 0

Solving
12 + 5u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -1u)(3 + 2u) = 0

Subproblem 1
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 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 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Subproblem 2
Set the factor '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 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 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {4, -1.5}