(z+3)(z+1)=15

Solution for (z+3)(z+1)=15 equation:

Simplifying
(z + 3)(z + 1) = 15

Reorder the terms:
(3 + z)(z + 1) = 15

Reorder the terms:
(3 + z)(1 + z) = 15

Multiply (3 + z) * (1 + z)
(3(1 + z) + z(1 + z)) = 15
((1 * 3 + z * 3) + z(1 + z)) = 15
((3 + 3z) + z(1 + z)) = 15
(3 + 3z + (1 * z + z * z)) = 15
(3 + 3z + (1z + z2)) = 15

Combine like terms: 3z + 1z = 4z
(3 + 4z + z2) = 15

Solving
3 + 4z + z2 = 15

Solving for variable 'z'.

Reorder the terms:
3 + -15 + 4z + z2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + 4z + z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + 4z + z2 = 0

Factor a trinomial.
(-6 + -1z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-6, 2}