(5u+3)(2+u)=0

Solution for (5u+3)(2+u)=0 equation:

Simplifying
(5u + 3)(2 + u) = 0

Reorder the terms:
(3 + 5u)(2 + u) = 0

Multiply (3 + 5u) * (2 + u)
(3(2 + u) + 5u * (2 + u)) = 0
((2 * 3 + u * 3) + 5u * (2 + u)) = 0
((6 + 3u) + 5u * (2 + u)) = 0
(6 + 3u + (2 * 5u + u * 5u)) = 0
(6 + 3u + (10u + 5u2)) = 0

Combine like terms: 3u + 10u = 13u
(6 + 13u + 5u2) = 0

Solving
6 + 13u + 5u2 = 0

Solving for variable 'u'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 5u)' equal to zero and attempt to solve:

Simplifying
3 + 5u = 0

Solving
3 + 5u = 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 + 5u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5u = 0 + -3
5u = 0 + -3

Combine like terms: 0 + -3 = -3
5u = -3

Divide each side by '5'.
u = -0.6

Simplifying
u = -0.6
Solution
u = {-2, -0.6}