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6x squared + 15x -9

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2 Answers

Hi Susan;
6x2 + 15x -9
3(2x2+5x-3)
We can set this equal to zero...
3(2x2+5x-3)=0
The parenthetical equation must equal zero.  Therefore, we can eliminate the 3...
2x2+5x-3=0
For the FOIL...
FIRST must be (2x)(x)=2x2
OUTER and INNER must add-up to 5x.
LAST must be (3)(1) or (1)(3) and either number must be negative to produce -3.
(2x-1)(x+3)
Let's FOIL...
FIRST...(2x)(x)=2x2
OUTER...(2x)(3)=6x
INNER...(-1)(x)=-1x=-x
LAST...(-1)(3)=-3
2x2+6x-x-3
2x2+5x-3
(2x-1)(x+3)=0
Either or both parenthetical equations must equal zero...
2x-1=0
2x=1
x=1/2
x+3=0
x=-3
You want to solve:
 
   6X^2 + 15X - 9 =0
 
    3 ( 2X^2 + 5X - 3 )
 
     3 ( 2X^2 + 6X - X -3 ) =0
 
       3 [ 2X( X +3 ) - ( X +3 ) ] =0
  
        3 [ ( X +3 ) ( 2X -1) ] =0
 
           X +3 = 0   X = -3    , 2X -1 = 0  X = 1/2