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Solving Equations by Factoring

This idea will work for algebra blobs too:

if ( x - 3 ) ( x + 2 ) = 0 either the first blob must be 0 or the second blob must be 0

So...

if ( x - 3 ) ( x + 2 ) = 0

then ( x - 3 ) = 0 or ( x + 2 ) = 0

Which is really just

x - 3 = 0 or x + 2 = 0

and we can easily solve these guys to get our answers:

x - 3 = 0 or x + 2 = 0 ... add 3 to both sides of the first equation and subtract 2 from both sides of the second equation, which gives x = 3 or x = -2

Guess what? We just solved this guy:

x^2 - x - 6 = 0 ... Factor: ( x - 3 ) ( x + 2 ) = 0 ... Blobs = 0: x - 3 = 0 or x + 2 = 0 ... solve: add 3 to both sides of the first equation and subtract 2 from both sides of the second equation, which gives x = 3 or x = -2 ... this "or" is kind of important since x cannot be 3 AND -2 at the same time!