Answer
$$x=3,\:x=-2$$
Work Step by Step
Solving by plugging in the given value and then using the quadratic formula, we find:
$$ 1\cdot \:x\left(x+3\right)=\frac{2}{x}x\left(x+3\right)+\frac{2}{x+3}x\left(x+3\right)\\ x\left(x+3\right)=2\left(x+3\right)+2x\\ x^2-x-6=0\\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\left(-6\right)}}{2\cdot \:1}\\ x=3,\:x=-2$$
