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Solve and Piecewise Functions


I was hoping something like this: 
   
   
  Clear["*"]
  g=Piecewise[{{0,x<0},{2 x-x^2,0<=x<4},{16 x-x^2,x³4}}]
  h=x-2;
  Solve[g?h,x]
   
   
  would give me a meaningful answer.  But all I get is this:
   
   
  Solve[\[Piecewise]{
  {0, x<0},
  {2 x-x2, 0£x<4},
  {16 x-x2, x³4}
  }?-2+x,x]
   
  Any thoughts on how to do this?


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