Question

What is the solution set to the equation (3x−9)(5x−3)=0?

Answer 1

This product could be zero if one or both of the parenthesis are zero.
3x-9=0; 3x=9; x= 3
5x-3=0; 5x=3; x=3/5

The solution is { 3/5, 3}

Answer 2

({3,\frac{3}{5} })

Explanation:

Given is an equation in x with two factors on left side and 0 on right side as

`(3x−9)(5x−3)=0`

We know that when product of two factors is zero, then any one of the factors can be 0

Equate each factor to 0

`(3x−9)=0\\(5x−3)=0\\x=3\\x=(3)/(5)`

Thus we have two solutions

x=3\\

x=\frac{3}{5}

Solution set is

`({3,(3)/(5) })`