Use factoring and the zero product property to solve the following:

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

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

The above function is already in the factorized form with z,(z+1) and (z+3) as factors.

`f(x) = z(z+1)(z+3)`

Using zero product property to f(x) = 0 we need either;

`z = 0`

`(z+1) = 0`

`(z+3) = 0`

*So the values of z that satisfy f(x) = 0 are;*

*z = 0*

*z = -1*

*z = -3*

**Sources:**

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

Since the product of the three factors, z, (z+1) and (z+3), equals zero one of the factors must equal zero according to the zero product property. Therefore either

z=0,z+1=0, or z+3=0

solve each equation for z and your answer is

z=0

z+1-1 =0-1 so z=-1

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

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