Does someone know Solve by factoring: 7x ( x - 1 ) = 1 - x?

7x² - 7x = 1 - x
7x² - 6x - 1 = 0
(7x + 1)(x - 1) = 0
x = - 1/7 , x = 1

OPTION b)

b) -1/7, 1
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Ideas: 7x ( x - 1 ) = 1 - x => (7x+1)(x-1) = 0

7x(x - 1) = 1 - x
7x^2 - 7x = 1 - x
7x^2 - 7x + x - 1 = 0
7x^2 - 6x - 1 = 0
(7x + 1)(x - 1) = 0

7x + 1 = 0
7x = -1
x = -1/7

x - 1 = 0
x = 1

∴ x = -1/7 , 1
(answer b)

7x ( x - 1 ) = 1 - x

This problem may be confusing because of the directions to solve by factoring
because
You must first set the equation equal to zero and in order to do that you must
first simplify each side separately
7x ( x - 1 ) = 1 - x
7x^2 - 7x = 1 - x
then set equal to zero
7x^2 - 6x - 1 = 0
Now factor the left side
( 7x + 1 )( x - 1 )=0
then zero product property
7x +1 = 0 or x - 1 = 0

therefore the right answer is b) -1/7, 1

7x ( x - 1 ) = 1 - x
7x^2 - 7x = 1-x
7x^2 - 6x -1 = 0
(7x - 7) (7x + 1) = 0
x = 1 or x = -1/7

So, the answer is B.

1) Distribute.
7x^2 - 7x = 1 - x

2) Move everything to one side by adding or subtracting by both sides of the equation.
7x^2 - 7x - 1 + x = 0
7x^2 - 6x - 1 = 0

3) Factor.
(7x + 1)(x - 1) = 0

4) Solve for x.
7x + 1=0 --> 7x = -1 --> x=-1/7
x - 1 = 0 --> x=1

x= -1/7, 1

So the answer is b.

First use the distributive property:

7x ( x - 1) = 1- x

7x ^ 2 - 7x = 1 - x

Then combine like terms on the left side so that the equation equals 0

7x^2 -6x - 1 = 0

Now you can you the quadratic equation but if this is a multiple choice test the plug in every answer for "x"
and if it equals 0 then its it.

Or if you know how to factor

(7x + 1 )(x - 1)= 0

then set each factor equal to 0

7x + 1 = 0 x = -1/7
x - 1 = 0 x = 1

so choose answer B