(2u-5)(8+u)=0

Solution for (2u-5)(8+u)=0 equation:

Simplifying
(2u + -5)(8 + u) = 0

Reorder the terms:
(-5 + 2u)(8 + u) = 0

Multiply (-5 + 2u) * (8 + u)
(-5(8 + u) + 2u * (8 + u)) = 0
((8 * -5 + u * -5) + 2u * (8 + u)) = 0
((-40 + -5u) + 2u * (8 + u)) = 0
(-40 + -5u + (8 * 2u + u * 2u)) = 0
(-40 + -5u + (16u + 2u2)) = 0

Combine like terms: -5u + 16u = 11u
(-40 + 11u + 2u2) = 0

Solving
-40 + 11u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-8 + -1u)(5 + -2u) = 0

Subproblem 1
Set the factor '(-8 + -1u)' equal to zero and attempt to solve:

Simplifying
-8 + -1u = 0

Solving
-8 + -1u = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1u = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1u = 0 + 8
-1u = 0 + 8

Combine like terms: 0 + 8 = 8
-1u = 8

Divide each side by '-1'.
u = -8

Simplifying
u = -8
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 = {-8, 2.5}