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Question 574101: solve using the principle of zero products.
(13c+7)(6c-18)=0
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! Are the words "principle of zero products" throwing you off? All that means is if we have two numbers or expressions that multiply to get zero, one of those MUST be zero. Could be both, but for sure one.
In that case, let's consider the equation you have:
(13c+7)(6c-18)=0
Looking at what I wrote above, either
(13c+7) OR (6c-18) must be zero (or both).
So let's see what happens then if we solve these individually:
(13c+7) = 0
13c + 7 = 0 Subtract 7 from both sides
13c = -7 Divide both sides by 13
c = -7/13 (Not my favorite kind of answer - it always makes me feel I did something wrong. But we'll check in a bit.)
(6c-18)=0
6c - 18 = 0 Add 18 to both sides:
6c = 18 Divide both sides by 6
c = 3
Checking:
(13c + 7)(6c - 18) = 0
(13(-7/13) + 7)(6(-7/13) - 18) = 0 Cancelling the 13 from numerator and denominator:
(-7 + 7)(-42/13 - 18) =0
(0)(-42/13 - 18) = 0 Good enough. Anything multiplied by 0 = 0
(13c + 7)(6c - 18) = 0
(13(3) + 7)(6(3) - 18) = 0
(39 + 7)(18 - 18) = 0
(46)(0) = 0
0 = 0 Correct!
Either c=-7/13 or c=3 are valid answers.
Hope the explanation helps too!
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