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That's an interesting derivation, I especially like the second line (I didn't notice that). But I don't understand how this is easier, or how we're "leaping off a bridge." I thought we were solving them algebraically. I suspect that your familiarity with math and symbols makes this more intuitive to you.
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What gumpzilla said about plugging in numbers. Make one small mistake and good luck finding it. Make a mistake in your symbolic algebra, and it is easy to find.
Also, his point about dimensions is really critically important every post in this thread had a bunch of dimensionless numbers in it (3000, 343, 0.75). This is *wrong*. All of the expressions written were dimensionally incorrect. By throwing out the units you throw out critical information that can allow you to catch and correct errors.
What if I had forgotten to multiply my answer by the speed of sound in concrete in the last step? I wouldn't even have something that had dimensions of distance; it would be a time instead:
It couldn't possibly be correct. If I don't keep track of my units, I have no way of catching such a mistake.