Question

How do you solve `(4x^2-4x-168)/(2x+12) = 20`?

Answer 1

`x=17`

Explanation:

First note that for the right side to be meaningful
`color(white)("XXX")color(red)(x!=-6)`

If this is true
`color(white)("XXX")(4x^2-4x-168)/(2x+12)=20`

`color(white)("XXX")rArr 4x^2-4x-168=40x+240`

`color(white)("XXX")rArr 4x^2-44x-408=0`

`color(white)("XXX")rArr x^2-11x-102=0`

We might be able to factor by inspection,
or using the Quadratic Formula
`color(white)("XXX")x=(11+-sqrt(121+408))/2 = (11+-sqrt(529))/2 =(11+-23)/2`

Giving
`color(white)("XXX")x=-6` ...but we have already noted that this is not permitted.
or
`color(white)("XXX")x=17`