Question

Using factoring and the zero-product property,please show how to solve the following problem:

z(z-1)(z+3)=0

Thank you for your help.

Answer 1

If any one of those three factors is zero, then the product is zero
so
z = 0 works

z-1 = 0 works so z = 1 works

z+3 = 0 works so z = -3 works

therefore
z = 0 or 1 or -3