SOLUTION: Can these be done? 3x^2 + 15x + 18 = 0 1 + 3y/y-2 = 6/y-2

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Question 53222: Can these be done?
3x^2 + 15x + 18 = 0
1 + 3y/y-2 = 6/y-2

Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
Use the "ac" method. Given an equation in the format ax%5E2%2Bbx%2Bc=0 where a%3C%3E1, then ac=3%2A18=54 in our case. Now we need to find two numbers that when multiplied together is 54 and when added together is 'b' in the equation above, or 15 for us. Make a table of the numbers: 2*27=54, but 2+27=29; 3*18=54, but 3+18=21; 6*9=54 and 6+9=15 --> we found them! So, with the 6 and 9, we use them as coefficients and break up 'bx', thusly: 3x%5E2%2B6x%2B9x%2B18=0. Now use grouping: %283x%5E2%2B6x%29%2B%289x%2B18%29=0. Now factor the two groupings: 3x%28x%2B2%29%2B9%28x%2B2%29=0. The factor (x+2) is common now and we can factor that out to get %28x%2B2%29%283x%2B9%29=0. That means that either x+2=0 or 3x+9=0. Solving both of them shows us that x=-2 or x=-3.