1/2/15 Purchased patent (6-year life) $521,580

4/1/15 Goodwill purchased (indefinite life) 395,170

7/1/15 14-year franchise; expiration date 7/1/2025 519,400

9/1/15 Research and development costs 169,890

Prepare the necessary entries to record these intangibles. All costs incurred were for cash. Make the adjusting entries as of December 31, 2015, recording any necessary amortization.

I know how to do the rest of the dates but need help, just don't know how to put in the entry for 12/31/15

To record the necessary entry for the intangibles as of December 31, 2015, you will need to make adjusting entries for any necessary amortization.

Let's break down the given information and calculate the amortization for each intangible asset:

1. Patent (6-year life):
The patent was purchased on 1/2/15, and its useful life is 6 years. Therefore, the remaining useful life of the patent at 12/31/15 is 6 - (12/31/15 - 1/2/15) = 5.958 years.

To record the amortization expense for the patent at 12/31/2015, you need to calculate the amortization amount:
Amortization Expense = (Patent Cost) / (Patent Life)
Amortization Expense = $521,580 / 6 = $86,930

The entry for the patent amortization on 12/31/15 is as follows:
Debit: Amortization Expense - Patent $86,930
Credit: Accumulated Amortization - Patent $86,930

2. Goodwill (indefinite life):
Since goodwill has an indefinite life, it does not get amortized. Therefore, no entry is needed for the goodwill as of 12/31/15.

3. Franchise (14-year life):
The franchise was purchased on 7/1/15, and its expiration date is 7/1/2025. Therefore, the remaining useful life of the franchise at 12/31/15 is 2025 - (12/31/15 - 7/1/15) = 10.5 years.

To record the amortization expense for the franchise at 12/31/2015, you need to calculate the amortization amount:
Amortization Expense = (Franchise Cost) / (Franchise Life)
Amortization Expense = $519,400 / 14 = $37,100

The entry for the franchise amortization on 12/31/15 is as follows:
Debit: Amortization Expense - Franchise $37,100
Credit: Accumulated Amortization - Franchise $37,100

Now you have recorded the necessary entries for the intangibles and made the relevant amortization adjustments as of December 31, 2015.