In an NLP paper there is the following equation that needs to be solved for x (I renamed some variables): $$y \cdot \frac{1}{1+e^{-x}}-k \cdot w \cdot \frac{c}{D} \cdot \frac{1}{1+e^{x}} = 0$$
In the paper at the bottom of page 3 they do some massive simplification in a single step which I do not understand:
$$ e^{2 x}-\left(\frac{y}{k \cdot w \cdot \frac{c}{D}}-1\right) e^x-\frac{y}{k \cdot w \cdot \frac{c}{D}}=0 $$