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

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

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

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

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

Combine like terms: 8u + 5u = 13u
(-20 + 13u + -2u2) = 0

Solving
-20 + 13u + -2u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-4 + u = 0

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

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

Combine like terms: 0 + 4 = 4
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}