35x² = 7x • 5x, and
5x (7x + 3) = 35x² + 15x
Subtract this from the dividend to get an initial remainder of
(35x² - 48x - 27) - (35x² + 15x) = -63x - 27
-63x = 7x • (-9), and
-9 (7x + 3) = -63x - 27
Subtract this from the previous remainder to get a new one of
(-63x - 27) - (-63x - 27) = 0
and we're done.
Now just gather the terms in bold (and the remainder, but since it's 0 we leave it out). So we have
(35x² - 48x - 27) / (7x + 3) = 5x - (63x + 27) / (7x + 3)
(35x² - 48x - 27) / (7x + 3) = 5x - 9
