SOLUTION: Solve by factoring and using the principle of zero products {{{(2x-9)(3x^2+26x+48)=0}}}

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Question 547294: Solve by factoring and using the principle of zero products
%282x-9%29%283x%5E2%2B26x%2B48%29=0
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-9%29%283x%5E2%2B26x%2B48%29=0
The Principle of Zero Factors just says that if a product is zero, then at least one of the factors is zero. This means that either
2x-9=0
2x=9
x=9%2F2
OR
%283x%5E2%2B26x%2B48%29=0
Using the quadratic formula we see that either
x=%28-26%2Bsqrt%2826%5E2-4%2A3%2A48%29%29%2F2%2A3
x=%28-26%2Bsqrt%28676-576%29%29%2F6
x=%28-26%2Bsqrt%28100%29%29%2F6
x=%28-26%2B10%29%2F6
x=%28-16%29%2F6
x=-8%2F3
or
x=%28-26-sqrt%2826%5E2-4%2A3%2A48%29%29%2F2%2A3
x=%28-26-sqrt%28676-576%29%29%2F6
x=%28-26-sqrt%28100%29%29%2F6
x=%28-26-10%29%2F6
x=%28-36%29%2F6
x=-6
Therefore there are three answers that would make the formula correct, x=-6, x=-8/3 and x=9/2

Hopefully this helps, let me know if you are still unsure:)