solving equation by factoring

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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 6x^{2} - 6x

combine the product 6x^{2} - 6x with = 21 - x

this will lead to 6x^{2} - 6x = 21 - x

rearrange as per like terms and exponents to give balance the equation....

6x^{2} - 6x **- 21** + x = 21
**- 21** - x + x ( this... 21 - 21 - x + x = zero )

rearrange due to like terms

6x^{2} - 6x - 21 + x ----> 6x^{2} - 6x + x - 21 or 6x^{2} - 3x - 21

Now...use the F O I L method to factor:

F(First) .....factors of 6x^{2} are 1, 2, 3, 6, and x^{2}, 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.

6x^{2}-6x=21-x

Let's move everything to the left side by subtracting (21-x) from both sides...

6x^{2}-6x-(21-x)=(21-x)-(21-x)

6x^{2}-6x-21+x=0

6x^{2}-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 6x^{2} ...

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.

6x^{2}-5x-21=0

( 7)( 3)

The rest is trial-and-error...

(3x-7)(2x+3)

FOIL

FIRST...6x^{2}

OUTER...9x

INNER...-14x

LAST...-21

6x^{2}+9x-14x-21=0

6x^{2}-5x-21=0

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