Find all values of $x$ such that $\dfrac{x}{x+4} = -\dfrac{9}{x+3}$. If you find more than one value, then list your solutions in increasing order, separated by commas.
x / (x + 4) = -9 / (x + 3) Numbers that cannot be answers: -4, -3
Cross multiply:
x(x + 3) = -9(x + 4)
x2 + 3x = -9x - 36
x2 + 3x + 9x + 36 = 0
x2 + 12x + 36 = 0
(x + 6)(x + 6) = 0
x = -6