3/(x+6)=-3/4
We are all mathematically retarded in one field or another.
So, continuing from where I left off...
Look at the left side of the equation, note how the $\displaystyle (x+6)s$ cancel leaving only
$\displaystyle 4\cdot3=\left(\frac{-3}{4}\right)4(x+6)$.
Now look at the right side, the fours cancel leaving
$\displaystyle 4\cdot3=-3(x+6)$.
This is why we multiplied by the LCD, to get rid of those nasty fractions.
Now, multiplying out the parentheses,
$\displaystyle 12=-3x-18$
adding 18 to both sides we get
$\displaystyle 30=-3x$
Finally, we divide each side by -3 and we are left with
$\displaystyle -10=x$