Factor
z^2 + 4z - 12
z^2 + 4z - 12
-
z^2 + 4z - 12
(z+6)(z-2)
if you cannot see factors
use the quadratic formula
first, the discriminant
b^2-4ac
16+48
64
+/-8
rest of q.f.
(-b+/-8)/2a
(-4+/-8)/2
4/2,-12/2
2, -6
extract the factors
set the factors equal to the variable
then solve for 0
z=2
z-2=0
(z-2)
z= -6
z+6=0
(z+6)
(z+6)(z-2)
p.s.
you can solve for circles as well
(z+6)(z-2)
if you cannot see factors
use the quadratic formula
first, the discriminant
b^2-4ac
16+48
64
+/-8
rest of q.f.
(-b+/-8)/2a
(-4+/-8)/2
4/2,-12/2
2, -6
extract the factors
set the factors equal to the variable
then solve for 0
z=2
z-2=0
(z-2)
z= -6
z+6=0
(z+6)
(z+6)(z-2)
p.s.
you can solve for circles as well
-
(z + 6)(z - 2)
-
z^2 + 4z - 12
(z + 6) (z - 2)
(z + 6) (z - 2)