How can I find a equivalent conditions for the following inequality
$$
0\leq x+\frac{1}{2}x(1-x)a\leq 1?
$$

This is from a numerical analysis book, *Finite-Volume Methods For Hyperbolic Problems*. I have no idea why this can be equivalent to 
$$
0\leq x\leq 1\qquad\text{and}~|a|\leq 2. 
$$

How can one come up with such conditions?