The area of a rectangular knitted blanket is 14 x^2 - 17 x -6. what are the possible dimensions of the blanket? use factoring.

It's unlikely that it the dimensions are either 14 and 1 in front of the x or 6 and 1 for the 6, but this is math, so you never know. I would try 7 and 2 and 3 and 2 and see what comes of it.

(7x        2)(2x     3 ) That looks promising. We'll put the 3 with the 2x. That leaves us with the signs. We need 17 to  be minus

(7x        2)(2x - 3) that gives you - 21 x So the 2 with the seven has to be plus.

(7x + 2)(2x - 3) should be the the factored answer.
7x + 2 = 0 has no meaning. Measurements cannot be minus.

2x - 3 = 0
2x = 3
x = 3/2

If there are choices, please list them.  That's as far as is possible.