Find plane equidistant between two points

Find an equation for the plane, each of whose points is equidistant from (-1, -4, -2) and (0, -2, 2).

I tried to work on this by setting two distance formulas equal to each other, but I didn't know how to handle the absolute value on both sides, and the d term kept canceling out.

Also, I'm really hoping the question is referring to *points* and not *vectors* using that notation.

$\displaystyle \frac{|-a-4b-2c+d|}{\sqrt{a^2 + b^2 +c^2}}=\frac{|-2b+2c+d|}{\sqrt{a^2 + b^2 +c^2}}$