help algebra

N^3  =  3N^2 * 2

N^3  - 6N^2  =  0

N^2  ( N - 6) =  0

N - 6  =  0

N = 6

If the cube of a positive number is three times the square of the number times two, what is the number?    

What I noticed was that         3 • n² • 2  is the same as  6 • n² 

And since                                        n³   is the same as  n • n²  

Then you could say that             6 • n²  =  n • n²  

From which follows that                      n  =  6  

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