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# 6x(x-1) = 21 - x

solving equation by factoring

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