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

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

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

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

Multiply (5 + u) * (1 + 5u)
(5(1 + 5u) + u(1 + 5u)) = 0
((1 * 5 + 5u * 5) + u(1 + 5u)) = 0
((5 + 25u) + u(1 + 5u)) = 0
(5 + 25u + (1 * u + 5u * u)) = 0
(5 + 25u + (1u + 5u2)) = 0

Combine like terms: 25u + 1u = 26u
(5 + 26u + 5u2) = 0

Solving
5 + 26u + 5u2 = 0

Solving for variable 'u'.

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

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

Simplifying
5 + u = 0

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

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

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

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

Simplifying
1 + 5u = 0

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

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

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

Divide each side by '5'.
u = -0.2

Simplifying
u = -0.2
Solution
u = {-5, -0.2}