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

Solution for (8+u)(5u+1)=0 equation:

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

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

Multiply (8 + u) * (1 + 5u)
(8(1 + 5u) + u(1 + 5u)) = 0
((1 * 8 + 5u * 8) + u(1 + 5u)) = 0
((8 + 40u) + u(1 + 5u)) = 0
(8 + 40u + (1 * u + 5u * u)) = 0
(8 + 40u + (1u + 5u2)) = 0

Combine like terms: 40u + 1u = 41u
(8 + 41u + 5u2) = 0

Solving
8 + 41u + 5u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(8 + u)' equal to zero and attempt to solve:

Simplifying
8 + u = 0

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

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

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

Simplifying
u = -8
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 = {-8, -0.2}