document.write( "Question 607930: Solve by factoring and using the principle of zero products:
\n" ); document.write( "3x^2+8x=9+2x
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Algebra.Com's Answer #382964 by jsmallt9(3758) $\"\"$ $\"About$

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$\"3x%5E2%2B8x=9%2B2x\"$
\n" ); document.write( "To have a zero product, we first have to have a zero. So we start by subtracting 9 and 2x from each side. This gives us:
\n" ); document.write( " $\"3x%5E2%2B6x-9=0\"$
\n" ); document.write( "We have the zero. Now we need a product. So we factor the left side. First, as always, factor out the GCF (which is 3):
\n" ); document.write( " $\"3%28x%5E2%2B2x-3%29+=+0\"$

\n" ); document.write( "Next we factor the trinomial. Since the $\"x%5E2\"$ has a coefficient of 1 we just have to ask ourselves: \"What are the factors of the constant (\"variable-less\") term (the -3) which add up to the middle coefficient (the 2)? The factors of -3 that add up to 2 are: 3 and -1. So we can factor the trinomial:
\n" ); document.write( "3(x+3)(x-1) = 0

\n" ); document.write( "Now that we have a zero product we can use the Zero Product Property (which is apprently being called the \"principle of zero products\" in your class) which tells us that this (or any) product can be zero only if one (or more) of the factors is zero. The 3 is a 3 and it cannot be zero. But the other two factors have a variable in them so they could be zero. So:
\n" ); document.write( "x + 3 = 0 or x - 1 = 0

\n" ); document.write( "Solving each of these we get:
\n" ); document.write( "x = -3 or x = 1
\n" ); document.write( "These are the solutions to your equation. \n" ); document.write( "

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