(5u+8)(3+u)=0

Solution for (5u+8)(3+u)=0 equation:

Simplifying
(5u + 8)(3 + u) = 0

Reorder the terms:
(8 + 5u)(3 + u) = 0

Multiply (8 + 5u) * (3 + u)
(8(3 + u) + 5u * (3 + u)) = 0
((3 * 8 + u * 8) + 5u * (3 + u)) = 0
((24 + 8u) + 5u * (3 + u)) = 0
(24 + 8u + (3 * 5u + u * 5u)) = 0
(24 + 8u + (15u + 5u2)) = 0

Combine like terms: 8u + 15u = 23u
(24 + 23u + 5u2) = 0

Solving
24 + 23u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + u)(8 + 5u) = 0

Subproblem 1
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(8 + 5u)' equal to zero and attempt to solve:

Simplifying
8 + 5u = 0

Solving
8 + 5u = 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 + 5u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5u = 0 + -8
5u = 0 + -8

Combine like terms: 0 + -8 = -8
5u = -8

Divide each side by '5'.
u = -1.6

Simplifying
u = -1.6
Solution
u = {-3, -1.6}