(X+1)(X+5)=0

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

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

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

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

Multiply (1 + X) * (5 + X)
(1(5 + X) + X(5 + X)) = 0
((5 * 1 + X * 1) + X(5 + X)) = 0
((5 + 1X) + X(5 + X)) = 0
(5 + 1X + (5 * X + X * X)) = 0
(5 + 1X + (5X + X2)) = 0

Combine like terms: 1X + 5X = 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}