For which values of z in the function f(z) positive? F(z) = (z-7)(z+5)

Given:
[tex]f(z)=(z-7)(z+5)[/tex]Multiply of two number is positive that mean both number is positive or both number is negative so:
For both positive :
[tex]z>7[/tex]For both negative :
[tex]z<-5[/tex]For function is positive
[tex]\begin{gathered} (-\infty,-5)\cup(7,\infty) \\ or \\ -5>z>7 \end{gathered}[/tex](B)
for function negative:
One factor is positive and another factor is negative:
[tex]-5