Question 294886
{{{3m^2 + 14m -5=(3m+a)(m+b)}}}
If you FOIL the right hand side, you get,
{{{(3m+a)(m+b)=3m^2+3bm+am+ab}}}
{{{(3m+a)(m+b)=3m^2+(3b+a)m+ab}}}
Comparing to your equation,
{{{3b+a=14}}}
{{{ab=-5}}}
Integer factors of 5 are 1 and 5.
{{{ a=1 }}}, {{{ b=-5}}}
{{{ a=-1}}}, {{{ b=5}}}
{{{ a=5}}}, {{{ b=-1}}}
{{{ a=-5}}}, {{{ b=1}}}
All of those combinations solve {{{ab=-5}}}
Now check using the other equation to see which one is correct.
{{{ a=1}}}, {{{ b=-5}}}
{{{3b+a=14)))
{{{3(-5)+1=14}}}
{{{-14=14}}}
No, next set.
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{{{ a=-1}}},{{{ b=5}}}
{{{3(5)-1=14}}}
{{{14=14}}}
That's the one. 
So then a=-1, b=5.
{{{3m^2 + 14m -5=(3m+a)(m+b)}}}
{{{3m^2 + 14m -5=(3m-1)(m+5)}}}