solving equation by factoring

Tutors, sign in to answer this question.

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

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Harry O.

Harry O: tutoring in ACT, algebra, geometry, physics and calculus

$12.50 per 15 min

View Profile >

Kevin K.

One stop shop for math, science and test prep!

$12.50 per 15 min

View Profile >

Majdi J.

Patient and knowledgable Math tutor .

$10 per 15 min

View Profile >