Question 77918
(3m-5)(m+7)=0
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If either of the two factors on the left side equals zero, then the left side becomes
zero. This is because multiplying anything by zero results in zero as the answer. And if
the left side is zero, then it equals the right side.
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Just as a further example in the way of explanation, suppose (3m - 5) equals zero, then the
equation becomes 0 * (m + 7) = 0. And this means that we need to find what value of m
will make 3m - 5 equal zero.  Now suppose (m + 7) equals zero.  This would make the 
equation become (3m - 5) * 0 = 0.  Note that this equation is true because the left side
is zero (due to the multiplication by zero) and, therefore, it equals the right side.
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So all you need to do for this problem is to set each of the factors equal and solve 
for m.
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3m - 5 = 0
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eliminate the -5 on the left side by adding 5 to both sides to get:
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3m = +5
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Then solve for m by dividing both sides by 3 to get:
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m = 5/3
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Next, we set the other factor equal to zero:
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m + 7 = 0
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eliminate the + 7 on the left side by subtracting 7 from both sides to get:
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m = -7
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There you have it ... two values of m will satisfy the original equation.  Those two values
for m are m = 5/3 and m = -7.
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And if you substitute those two values for m into the original equation you will see 
that they work.
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Hope this helps you to understand the problem.