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

Solution for (2u-1)(5+u)=0 equation:

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

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

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

Combine like terms: -1u + 10u = 9u
(-5 + 9u + 2u2) = 0

Solving
-5 + 9u + 2u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve:

Simplifying
-5 + -1u = 0

Solving
-5 + -1u = 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 + -1u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1u = 0 + 5
-1u = 0 + 5

Combine like terms: 0 + 5 = 5
-1u = 5

Divide each side by '-1'.
u = -5

Simplifying
u = -5
Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 0

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

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

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-5, 0.5}