Team $A$ is playing team B in a series of three games. Team $A$'s probability of winning any particular game is nonzero, independent of other games, and is $1.6$ times as large as its probability of winning the series. What is the probability of team $A$ winning the series?
My approach :
Let the probability of winning any game be $x$, then $$x = 1.6 \left( x^3 + 3x(1 -x) \right)$$ because the series can be won as WWW, WLW, LWW, WWL.