(2u+5)(4-u)=0

Solution for (2u+5)(4-u)=0 equation:

Simplifying
(2u + 5)(4 + -1u) = 0

Reorder the terms:
(5 + 2u)(4 + -1u) = 0

Multiply (5 + 2u) * (4 + -1u)
(5(4 + -1u) + 2u * (4 + -1u)) = 0
((4 * 5 + -1u * 5) + 2u * (4 + -1u)) = 0
((20 + -5u) + 2u * (4 + -1u)) = 0
(20 + -5u + (4 * 2u + -1u * 2u)) = 0
(20 + -5u + (8u + -2u2)) = 0

Combine like terms: -5u + 8u = 3u
(20 + 3u + -2u2) = 0

Solving
20 + 3u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -1u)(5 + 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 '(5 + 2u)' equal to zero and attempt to solve:

Simplifying
5 + 2u = 0

Solving
5 + 2u = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2u = 0 + -5
2u = 0 + -5

Combine like terms: 0 + -5 = -5
2u = -5

Divide each side by '2'.
u = -2.5

Simplifying
u = -2.5
Solution
u = {4, -2.5}