Answer:
[tex]\large\boxed{(z-9)(z+8)=0\to z=9,\ z=-8}[/tex]
Step-by-step explanation:
[tex](z-5)(z+4)=52\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\(z)(z)+(z)(4)+(-5)(z)+(-5)(4)=52\\\\z^2+4z-5z-20=52\qquad\text{subtract 52 from both sides}\\\\z^2-z-72=0\\\\z^2-9z+8z-72=0\\\\z(z-9)+8(z-9)=0\\\\(z-9)(z+8)=0\iff z-9=0\ \vee\ z+8=0\\\\z=9\ \vee\ z=-8[/tex]
