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