Question 757114
Just helping with this one:  {{{7x^2 - 43x - 42 = 0}}}


Requiring two binomials, one with leading term 7x and other with leading term x.
The -42 contant term in the trinomial means you need to find which factorizations of -42 will make the two binomials work.


42=2*21
42=6*7
42=3*14
maybe also 42=1*42


You may need 6 to 8 combinations to try.  You could also try synthetic division if you know it, but not likely if you're just in Algebra 1.


Trying:  (7x_____2)(x____21_)
2x and 63x ?
No, not work.


Try:  (7x_____21)(x_____2)
21x and 14x
No.


Try:  (7x____3)(x____14)
3x and 98x
NO.


Try:    (7x_____14)(x_____3)
7x and 14x
Not useful.


Try:  (7x____6)(x_____7)
6 and 49
Looks like might work.
NOW Which sign goes where?  You want 6 and 49 somehow to give you -43.