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

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

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

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

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

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

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = -1x + -1

Reorder the terms:
3 + 4x + x2 = -1 + -1x

Solving
3 + 4x + x2 = -1 + -1x

Solving for variable 'x'.

Reorder the terms:
3 + 1 + 4x + x + x2 = -1 + -1x + 1 + x

Combine like terms: 3 + 1 = 4
4 + 4x + x + x2 = -1 + -1x + 1 + x

Combine like terms: 4x + x = 5x
4 + 5x + x2 = -1 + -1x + 1 + x

Reorder the terms:
4 + 5x + x2 = -1 + 1 + -1x + x

Combine like terms: -1 + 1 = 0
4 + 5x + x2 = 0 + -1x + x
4 + 5x + x2 = -1x + x

Combine like terms: -1x + x = 0
4 + 5x + x2 = 0

Factor a trinomial.
(4 + x)(1 + 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 '(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 = {-4, -1}