solving equation by factoring
6x(x-1) = 21 - x
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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=0 and 2x+3=0
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
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...
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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.
Let's move everything to the left side by subtracting (21-x) from both sides...
To factor this, we must consider all the number we can multiply together to reach -21...
-7 x 3
7 x -3
We must also consider all the options we have to reach 6x2 ...
6x times x
3x times 2x
-6x times -x
-3x times -2x
We must select one of the above combinations to reach -5x.
( 7)( 3)
The rest is trial-and-error...