Question 137956
{{{10x^2-17x=63}}}


First put the equation into standard form:
{{{10x^2-17x-63=0}}}


If this thing factors, the lead terms of the binomials must be 2x and 5x or x and 10x, and the constant terms of the binomials must be +9 and -7 or -9 and +7.  A bit of trial and error gets you to {{{(2x-7)(5x+9)=0}}}


You should be able to take it from here using the Zero Product Rule: {{{ab=0}}} if and only if {{{a=0}}} or {{{b=0}}}.