(z+7)(z+5)=0

Solution for (z+7)(z+5)=0 equation:

Simplifying
(z + 7)(z + 5) = 0

Reorder the terms:
(7 + z)(z + 5) = 0

Reorder the terms:
(7 + z)(5 + z) = 0

Multiply (7 + z) * (5 + z)
(7(5 + z) + z(5 + z)) = 0
((5 * 7 + z * 7) + z(5 + z)) = 0
((35 + 7z) + z(5 + z)) = 0
(35 + 7z + (5 * z + z * z)) = 0
(35 + 7z + (5z + z2)) = 0

Combine like terms: 7z + 5z = 12z
(35 + 12z + z2) = 0

Solving
35 + 12z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + z)(5 + 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 '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {-7, -5}