We know that one set of parentheses will be
#(2m+a)#
and the other will have to be
#(m+b)#
(Note: #a# and #b# are not the values from the equation, they are placeholders while solving)
So far we have:
#(2m+a)(m+b)=0#
Now let's find #a# and #b#
We know that #a*b=5*# because when you FOIL they have to multiply to equal #5#. Therefore, we know that one of them equals #5# and the other equals #1# because #5# is prime so those are its only factors.
We also know that #2m*b+a*m = 11m#. This can only be true if #b=5# and #a=1#. Now that we have found our values, let's solve for #m#.
#(2m+1)(m+5)=0#
Let's examine the first set of parentheses. We know that
#(2m+1)=0#
Subtract #1# from each side
#2m=-1#
Now divide each side by #2#
#m=-1/2#
Now, let's examine the second set of parentheses. We know that
#(m+5)=0#
Subtract #5# from each side
#m=-5#
Final answer:
#m=-5,-1/2#
