Hi Irish;

z

^{2}+2z-15=0For the FOIL...

FIRST must be (z)(z)=z

^{2}OUTER and INNER must add-up to 2z.

LAST must be (15)(1) or (1)(15) or (5)(3) or (3)(5) and one number must be negative to render the product of -15 and sum of +2.

(z+5)(z-3)=0

Let's FOIL...

FIRST...(z)(z)=x

^{2}OUTER...(z)(-3)=-3z

INNER...(5)(z)=5z

LAST...(5)(-3)=-15

z

^{2}-3z+5z-15=0z

^{2}+2z-15=0(z+5)(z-3)=0

Either or both parenthetical equation(s) must equal zero...

z+5=0...........z-3=0

**z=-5**.............

**z**

**=3**

Let's check our results...

z

^{2}+2z-15=0.....................z^{2}+2z-15=0z=-5...............................z=3

(-5)

^{2}+[(2)(-5)]-15............(3)^{2}+[(2)(3)]-15=025-10-15=0......................9+6-15=0

0=0.................................0=0