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

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

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

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

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

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

Combine like terms: 1u + 5u = 6u
(5 + 6u + u2) = 0

Solving
5 + 6u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + u)(1 + u) = 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 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Solution
u = {-5, -1}