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Back to the problem: (Where were we?)

Oh yeah!

Finish the subtraction!

7x - 10x = -3x


subtracting gives -3x ... now, we see how many times x goes into -3x

-3x / x = -3 ... this gives a quotient of 2x - 3


bring the -15 down, giving -3x - 15 under the dividend


multiply -3 to ( x + 5 ) ... subtract the product ( -3x - 15 ) under the  -3x - 15 we got in the last step ... this gives 0 ... when you hit 0 and there are no guys in the divident to bring down, you're done!

So, 

( 2x^2 + 7x - 15 ) / ( x + 5 ) = 2x - 3

Check it by multiplying!

( 2x - 3 ) ( x + 5 ) = 2x^2 + 10x - 3x - 15 = 2x^2 + 7x - 15 ... yep!