To solve the equation [tex]\((z-7)(z-2)=0\)[/tex], we can apply the Zero Product Property. This property states that if the product of two factors is zero, then at least one of the factors must be zero.
Here are the steps to solve for [tex]\(z\)[/tex]:
1. Set each factor equal to zero:
[tex]\[
(z - 7) = 0 \quad \text{or} \quad (z - 2) = 0
\][/tex]
2. Solve each equation separately:
- For the equation [tex]\((z - 7) = 0\)[/tex]:
[tex]\[
z - 7 = 0 \implies z = 7
\][/tex]
- For the equation [tex]\((z - 2) = 0\)[/tex]:
[tex]\[
z - 2 = 0 \implies z = 2
\][/tex]
3. Combine the solutions:
The solutions to the equation [tex]\((z-7)(z-2)=0\)[/tex] are [tex]\(z = 7\)[/tex] and [tex]\(z = 2\)[/tex].
Therefore, the solutions to the equation [tex]\((z-7)(z-2)=0\)[/tex] are [tex]\(\boxed{7 \text{ and } 2}\)[/tex].
