(x+3)(x+1)=0

Solution for (x+3)(x+1)=0 equation:

Simplifying
(x + 3)(x + 1) = 0

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

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

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 0
((1 * 3 + x * 3) + x(1 + x)) = 0
((3 + 3x) + x(1 + x)) = 0
(3 + 3x + (1 * x + x * x)) = 0
(3 + 3x + (1x + x2)) = 0

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 0

Solving
3 + 4x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
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 = {-3, -1}