AMC 12 2016a Problem 7

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

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