Question

How do you solve `4(3n - 2) (4n + 1) = 0`?

Answer 1

`n=2/3 and -1/4`

Explanation:

You can interpret the equation this way:
The product is 0 when you multiply the three factors 4, (3n-2), and (4n+1). Therefore, either of the three factors must be zero to make the statement true.

you can see it this way
`(4)\cdot(0)\cdot(4n+1)=0`
or
`(4)\cdot(3n-2)\cdot(0)=0`
or
`(4)\cdot(0)\cdot(0)=0`

Which means to say, that the factor `(3n-2)` and/or `(4n+1)` should be zero.

So,
`3n-2=0`
`=>3n=2`
`=>n=2/3`

Also,
`4n+1=0`
`=>4n=-1`
`=>n=-1/4`

Therefore, `n=2/3 and -1/4`

Another method is to expand the whole expression and perform long division. you should arrive with the same answer.