Question

What are the solutions to the equation (2x - 5)(3x - 1) = 0?

Answer 1

`\: x =2 (1)/(2) \: or \: x = (1)/(3)`

EXPLANATION

The equation is given in the factored form as:

`(2x - 5)(3x - 1) = 0`

According to zero product principle

`either \: \: (2x - 5) = 0 \: or \: (3x - 1) = 0`

This implies that,

`either \: \: 2x = 5 \: or \: 3x = 1`

We divide the first equation by 2 and the second by 3

`either \: \: x = (5)/(2) \: or \: x = (1)/(3)`

The solutions are

`\: x =2 (1)/(2) \: or \: x = (1)/(3)`

Answer 2

The solution of the given equation is (5/2, 1/3)

Explanation:

It is given an equation,

(2x - 5)(3x - 1) = 0

To find the solution of given equation

(2x - 5)(3x - 1) = 0 means that,

either (2x - 5) = 0 or (3x - 1) = 0

If 2x - 5 = 0

2x = 5

x = 5/2

or 3x - 1 = 0

3x = 3

x = 1/3

Therefore the solution of the given equation is (5/2, 1/3)