2016 AMC 12A Problem 7

Which of these describes the graph of x^2(x+y+1)=y^2(x+y+1) ?

\begin{array}{l} \textbf{(A)}\ \text{two parallel lines}\\ \qquad\textbf{(B)}\ \text{two intersecting lines}\\ \qquad\textbf{(C)}\ \text{three lines that all pass through a common point}\\ \qquad\textbf{(D)}\ \text{three lines that do not all pass through a common point}\\ \qquad\textbf{(E)}\ \text{a line and a parabola} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.