Question 855115
(7x+1)(x-7)   will not give the trinomial quadratic expression in your equation.


If you want to factor the left side of {{{7x^2-7x-1=0}}}, then you can try to look for two number whose sum is -7 and whose product is -1.  Try to arrange a form,  (7x__a)(x___b).  Can some combination be found?  Integers?


There is the complication that coefficient on the x^2 term must be 7; no matter - we look for combinations of numbers at least which give -1 product.


(7x___)(x___) and we can only use 1 and -1.  We have two ways to do this.
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{{{(7x-1)(x+1)=7x^2-1x+7x-1}}} ------ does not give us the quadratic we want.
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{{{(7x+1)(x-1)=7x^2+x-7x-1}}}-------still does not give us the quadratic we want.


USE THE GENERAL SOLUTION TO A QUADRATIC FORMULA.
Instead of carrying those solution steps for your example, I refer to a lesson about solving quadratic equations using completing the square or the general solution.
<a href="http://www.algebra.com/tutors/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">Solve a Quadratic Equation using the General Solution</a>