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6x(x-1) = 21 - x

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3 Answers

6x(x-1)=21-x
6x^2-6x=21-x
6x^2-6x+x-21=0
6x^2-5x-21=0
factor 6 into 3*2 and factor 21 into 7*3
group the 3 with the 3 and the 2 with the 7 to get 3*3=9 and 2*7=14
14-9=5(the middle term disregarding signs)
(3x-7)(2x+3)=0
3x-7=0 and 2x+3=0
3x=7, x=7/3
2x=-3, x=-3/2
Begin with multiplying   6x(x - 1)  this equals 6x2 - 6x
        combine the product 6x2 - 6x with  =  21 - x
        this will lead to   6x2 - 6x = 21 - x
        rearrange as per like terms and exponents to give    balance the equation....
                         6x2 - 6x - 21 + x = 21 - 21 - x + x       (   this...  21 - 21 - x + x  =  zero  )
           rearrange due to like terms
                           6x2 - 6x - 21 + x    ---->    6x2 - 6x + x - 21    or     6x2 - 3x - 21
         Now...use the F O I  L method to factor:
            F(First)    .....factors of 6x2  are   1, 2, 3, 6, and x2, and x
           O(Outer)
           I(Inner)
           L(Last)       ....factors of   -21 are 1, -1, 3, -3, 7, -7, 21, and -21
 
        okay....there are the tools...I've laid them out for you...work it out so you can practice and
         know how to solve these problems... your answer will look something like....
                      (    +    ) (    -    )   with the factors in the parenthesis...you work it out...
                                                    I have the answer...but want you to work it yourself
                                                     go to it...email me it you need further assistance
 
Hi Carla;
Thank you for another great question!
 
6x(x-1) = 21 - x
 
Let's discard the parentheses as we will soon factor and have a new set of parentheses.
 
6x2-6x=21-x
 
Let's move everything to the left side by subtracting (21-x) from both sides...
 
6x2-6x-(21-x)=(21-x)-(21-x)
 
6x2-6x-21+x=0
 
6x2-5x-21=0
 
To factor this, we must consider all the number we can multiply together to reach -21...
-7 x 3
or
7 x -3
 
 
We must also consider all the options we have to reach 6x2 ...
6x times x
or
3x times 2x
or
-6x times -x
or
-3x times -2x
 
We must select one of the above combinations to reach -5x.
 
6x2-5x-21=0
 
(       7)(      3)
 
The rest is trial-and-error...
(3x-7)(2x+3)
 
FOIL
FIRST...6x2
OUTER...9x
INNER...-14x
LAST...-21
 
6x2+9x-14x-21=0
6x2-5x-21=0