You can put this solution on YOUR website!
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First notice that 3 is a common factor of all three terms on the left side. Factor it
out and the left side becomes:
.
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Now divide both sides of the equation by 3 and the result is:
.
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Since the coefficient (multiplier) of the term is 1, you can ask yourself,
"What are the factors of 12 that might add together to give me the -7 on the middle term?"
(Notice that the factors of 12 have to either both be positive or both be negative
since they need to multiply together to give +12.)
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How about -3 and -4? They will multiply together to give you +12 and they will add together
to give you -7.
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That works. Therefore, the two factors are (x - 3) and (x - 4). If you multiply them
the result will be and that is what we were looking for.
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So now the problem is reduced to:
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This equation will be true if either of the factors is zero. Therefore, you know that either:
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or
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If you solve these two equations, you will get two answers ... x = 3 and x = 4. These are
the two values of x that will make your original equation true ... substitute 3 for x
and see if it doesn't make the left side of the original equation equal zero. Then
substitute 4 for x and see if that also doesn't make the left side of the original
equation equal zero.
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Hope this helps you to see how you can solve this equation by applying some basic rules
of algebra.
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