+42 Find all values of such that
\(\frac{2x}{x + 2} = -\frac{6}{x + 4}\)
If you find more than one value, then list your solutions, separated by commas.
+179 Cross multiply (multiply the numerator and denominator of opposite sides and vice versa.)
This gives us $2x(x+4) = -6(x+2) \rightarrow 2x^2+8x = -6x-12 \rightarrow 2x^2+14x+12 = 0 \rightarrow x^2+7x+6 = 0$.
Now we have to look for two numbers that add to $7$ and multiply to $6$. These numbers are clearly $1$ and $6$, so we can rewrite our equation as $(x+1)(x+6) = 0$. Thus, our answers are $\boxed{x = -1,-6}$.
