(z+3)(z+1)=0

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

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

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

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

Multiply (3 + z) * (1 + z)
(3(1 + z) + z(1 + z)) = 0
((1 * 3 + z * 3) + z(1 + z)) = 0
((3 + 3z) + z(1 + z)) = 0
(3 + 3z + (1 * z + z * z)) = 0
(3 + 3z + (1z + z2)) = 0

Combine like terms: 3z + 1z = 4z
(3 + 4z + z2) = 0

Solving
3 + 4z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
3 + z = 0

Solving
3 + z = 0

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

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

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

Add '-1' to each side of the equation.
1 + -1 + z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z = 0 + -1
z = 0 + -1

Combine like terms: 0 + -1 = -1
z = -1

Simplifying
z = -1
Solution
z = {-3, -1}