Question

solve.
-2z(z - 3)(z - 4) = 0
(if there is more than one solution, separate them with commas.)
z =

Explanation:

Step1: Apply Zero-Product Property

The equation is \(-2z(z - 3)(z - 4)=0\). By the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b=0\). So we set each factor equal to zero:

• For \(-2z=0\):

Step2: Solve for z from \(-2z = 0\)

Divide both sides of the equation \(-2z=0\) by \(- 2\). We get \(z=\frac{0}{-2}=0\).

• For \(z - 3=0\):

Step3: Solve for z from \(z - 3=0\)

Add 3 to both sides of the equation \(z - 3=0\). We get \(z=3\).

• For \(z - 4=0\):

Step4: Solve for z from \(z - 4=0\)

Add 4 to both sides of the equation \(z - 4=0\). We get \(z = 4\).

Answer:

\(0,3,4\)