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

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

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

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

Multiply (5 + 4u) * (2 + -1u)
(5(2 + -1u) + 4u * (2 + -1u)) = 0
((2 * 5 + -1u * 5) + 4u * (2 + -1u)) = 0
((10 + -5u) + 4u * (2 + -1u)) = 0
(10 + -5u + (2 * 4u + -1u * 4u)) = 0
(10 + -5u + (8u + -4u2)) = 0

Combine like terms: -5u + 8u = 3u
(10 + 3u + -4u2) = 0

Solving
10 + 3u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + -1u)(5 + 4u) = 0

Subproblem 1
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Subproblem 2
Set the factor '(5 + 4u)' equal to zero and attempt to solve:

Simplifying
5 + 4u = 0

Solving
5 + 4u = 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 + 4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4u = 0 + -5
4u = 0 + -5

Combine like terms: 0 + -5 = -5
4u = -5

Divide each side by '4'.
u = -1.25

Simplifying
u = -1.25
Solution
u = {2, -1.25}