"explained briefly" is correct and usable in written English.
You can use it when you need to summarize or explain something in a short amount of time or using minimal words. For example, "She explained briefly how to use the new software."
How we got into the mess we're in, explained briefly and brilliantly.
For the purposes of this article, the origins of conductivity in ceramics may be explained briefly.
The chemical composition of phenol and formaldehyde and their combination into networks of permanently interlinked large molecules are explained briefly in the article aldehyde condensation polymer.
Of these the simplest and most important theoretically (though not always the easiest to apply in practice) is the method of truth tables, which will now be explained briefly.
The traditional Roman Catholic view of the effectiveness of the sacraments (as defined by the Council of Trent) is described by the phrase ex opere operato ("from the work done"), which is best explained briefly by saying that the faith and virtue of the minister neither add to the sacrament by their presence nor detract from it by their absence.
Each of these sources is explained briefly below.
Once the web is complete, allow time to explain briefly an overview of the Palestinian-Israeli conflict.
Yet it has happened, and, as I try to explain briefly in the book, why it happened is harder to understand than you might think.
Just before takeoff, his father asks what keeps the plane up in the air & he explains briefly Bernoulli's theorem to him.
If you're interested in taking part, please post a comment below and explain briefly why the videos' producers should pick you.
As a preparation, we explain briefly Fourier series expansion.
