Here is the item again:
As he scrubbed the tile grout with a toothbrush and bleach. Nick vowed never again to let the bathroom get so filthy.

You chose to use Punctuation Rule 2 to fix the problem:

Subordinate Clause + , + Main Clause.

Here is the correction:

As he scrubbed the tile grout with a toothbrush and bleach, Nick vowed never again to let the bathroom get so filthy.

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