Question 1127489

{{{x^2 -y^2 + mx + 5y -6 = (ax + by +c)(dx + ey + f)}}}...first multiply right side of equation

{{{x^2 -y^2 + mx + 5y -6 = adx^2 +bey^2+(af+cd)x+(ae+bd)xy+(bf+ce)y+cf}}}


compare coefficients and you see that:


{{{ad=1}}}->only when {{{a=1}}} and {{{d=1}}}

{{{be=-1}}}->only when {{{b=-1}}} and {{{e=1}}}

{{{-m=af+cd}}}....since {{{a=1}}} and {{{d=1}}}

{{{-m=f+c}}}....eq.1

{{{ae+bd=0}}} since there is no {{{xy}}} term on left side

{{{cf=-6}}} ...only if {{{c=3}}} and {{{f=-2}}} or {{{c=1}}} and {{{f=-6}}} or vice versa

I will go with {{{c=3}}} and {{{f=-2}}}

then 

{{{-m=f+c}}}....eq.1
{{{-m=-2+3}}}
{{{-m=1}}}
{{{m=-1}}}

so, your solutions are: 
 
{{{a=1}}}
{{{b=-1}}}
{{{c=3}}}
{{{d=1}}}
{{{e=1}}}
{{{f=-2}}}
{{{m=-1}}}