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

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

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

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

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

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

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

Solving
3 + 4x + x2 = -1

Solving for variable 'x'.

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

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

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

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

Subproblem 1
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
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 = {-2, -2}