remember, you can do anything to an equation as long as you do it to both sides
so
get all the z on one side
add 4z to both sides
1=bz+4z+c
minus c bot sides
1-c=bz+4z
undistriibute z
1-c=z(b+4)
divide both sides by b+4
[tex]\frac{1-c}{b+4}=z[/tex]
[tex]z=\frac{1-c}{b+4}[/tex]