(z+7)(z+1)=0

Solution for (z+7)(z+1)=0 equation:

Simplifying
(z + 7)(z + 1) = 0

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

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

Multiply (7 + z) * (1 + z)
(7(1 + z) + z(1 + z)) = 0
((1 * 7 + z * 7) + z(1 + z)) = 0
((7 + 7z) + z(1 + z)) = 0
(7 + 7z + (1 * z + z * z)) = 0
(7 + 7z + (1z + z2)) = 0

Combine like terms: 7z + 1z = 8z
(7 + 8z + z2) = 0

Solving
7 + 8z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

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

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7
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 = {-7, -1}