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

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

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

Combine like terms: 5u + u = 6u
(6u)(2u + 1) = 0

Remove parenthesis around (6u)
6u(2u + 1) = 0

Reorder the terms:
6u(1 + 2u) = 0
(1 * 6u + 2u * 6u) = 0
(6u + 12u2) = 0

Solving
6u + 12u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6u'.
6u(1 + 2u) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
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 = {0, -0.5}