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To factor using decomposition, you need to find factors of the product of the first and last coefficient that sum to the middle coefficient.
In this case, you are looking for factors of 6x2=12 that sum to 13. This gives factors of 12 and 1.
Then split the middle term up using these coefficients. Finally, use factoring by grouping on the resulting expression twice.
For this expression, we get:
`6m^2+13mn+2n^2` split middle term using factors 12 and 1
`=6m^2+12mn+mn+2n^2` factor by grouping
`=6m(m+2n)+n(m+2n)` factor again
The expression factors to `(m+2n)(6m+n)` .