How many ordered pairs of positive real numbers (a,b) satisfy the equation
(1+2a)(2+2b)(2a+b)=32ab?<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>an infinite number