To solve the equation [tex]\((3x - 5)(2x - 10) = 0\)[/tex], we need to set each factor in the equation to zero and solve for [tex]\(x\)[/tex] individually. This is because a product of two terms is zero if and only if at least one of the terms is zero.
1. Solve the first factor:
[tex]\[
3x - 5 = 0
\][/tex]
Add 5 to both sides:
[tex]\[
3x = 5
\][/tex]
Divide by 3:
[tex]\[
x = \frac{5}{3}
\][/tex]
2. Solve the second factor:
[tex]\[
2x - 10 = 0
\][/tex]
Add 10 to both sides:
[tex]\[
2x = 10
\][/tex]
Divide by 2:
[tex]\[
x = 5
\][/tex]
So, the solution set of the equation [tex]\((3x - 5)(2x - 10) = 0\)[/tex] is [tex]\(\left\{ \frac{5}{3}, 5 \right\}\)[/tex].
Hence, the correct answer is:
[tex]\[
\left\{5, \frac{5}{3}\right\}
\][/tex]
