  We construct N-soliton solutions to the equation called Q3 in the recent
Adler-Bobenko-Suris classification. An essential ingredient in the construction
is the relationship of $(Q3)_{\delta=0}$ to the equation proposed by Nijhoff,
Quispel and Capel in 1983 (the NQC equation). This latter equation has two
extra parameters, and depending on their sign choices we get a 4-to-1
relationship from NQC to $(Q3)_{\delta=0}$. This leads to a four-term
background solution, and then to a 1-soliton solution using a Backlund
transformation. Using the 1SS as a guide allows us to get the N-soliton
solution in terms of the tau-function of the Hirota-Miwa equation.
