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

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

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

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

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

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

Combine like terms: -5z + 7z = 2z
(-35 + 2z + z2) = 0

Solving
-35 + 2z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(5 + -1z) = 0

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

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 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 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

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