The search for a missing retired Brisbane teacher's remains, who is believed to have been dumped in a garbage bin, could take weeks or months.

Police believe 78-year-old Lesley Trotter's body was dumped in a general waste wheelie bin on Maryvale Street in Toowong near where she lives on March 28.

Foul play cannot be ruled out, police said.

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Police Commissioner Katarina Carroll said the search through waste facilities for Trotter's body is going to be "tough going".

"(Police) have done an extraordinarily good job of isolating the areas that have to be searched," she said.

"Now the tough job starts of searching those areas thoroughly and, look, that might take days, but I've seen investigations like this in the past that take weeks."

The investigation could take months, Carroll warned, adding the discovery of her body could hold the key to finding out what happened to the retired teacher. 

"When you get the body of a person, you then have a lot more information available to you in terms of evidence and the forensics," she said.

"So, it's incredibly important that we do as much as we can in the next few weeks to find her."

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Detective Superintendent Andrew Massingham said last week the rubbish truck that allegedly picked up Trotter's body last month was taken to Nudgee Transfer Station where the rubbish was dropped into a pit before an additional 22 trucks visited the site that day.

The loads from each of the trucks were compressed and taken away from the site in six B-double semi-trailers.

The trucks then took the loads to dump sites at Rochedale and Swanbank.

Police will commence an "extensive search" of both sites to try and recover Trotter's remains later this week.

Officers currently have no suspects in their investigation.

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