(x+5)(x+1)=0

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

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

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

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

Multiply (5 + x) * (1 + x)
(5(1 + x) + x(1 + x)) = 0
((1 * 5 + x * 5) + x(1 + x)) = 0
((5 + 5x) + x(1 + x)) = 0
(5 + 5x + (1 * x + x * x)) = 0
(5 + 5x + (1x + x2)) = 0

Combine like terms: 5x + 1x = 6x
(5 + 6x + x2) = 0

Solving
5 + 6x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

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