6x(x-1) = 21 - x

Question

solving equation by factoring

Answer 1

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

Answer 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

 

Answer 3

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