(x+1)(x+5)=-3

Solution for (x+1)(x+5)=-3 equation:

Simplifying
(x + 1)(x + 5) = -3

Reorder the terms:
(1 + x)(x + 5) = -3

Reorder the terms:
(1 + x)(5 + x) = -3

Multiply (1 + x) * (5 + x)
(1(5 + x) + x(5 + x)) = -3
((5 * 1 + x * 1) + x(5 + x)) = -3
((5 + 1x) + x(5 + x)) = -3
(5 + 1x + (5 * x + x * x)) = -3
(5 + 1x + (5x + x2)) = -3

Combine like terms: 1x + 5x = 6x
(5 + 6x + x2) = -3

Solving
5 + 6x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
5 + 3 + 6x + x2 = -3 + 3

Combine like terms: 5 + 3 = 8
8 + 6x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
8 + 6x + x2 = 0

Factor a trinomial.
(4 + x)(2 + x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-4, -2}