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

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

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

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

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

Combine like terms: 5u + 4u = 9u
(10 + 9u + 2u2) = 0

Solving
10 + 9u + 2u2 = 0

Solving for variable 'u'.

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

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

Simplifying
2 + u = 0

Solving
2 + u = 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 + u = 0 + -2

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

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

Simplifying
u = -2
Solution
u = {-2.5, -2}