This is called the "ac method."

Multiply the coefficient of the quadratic term by the constant term. In this case

Now write all the possible factors of 6 in pairs:

1, 6

2, 3 <-- We don't need to do 3, 2 and 6, 1. They are considered repeats.

-1, -6

-2, -3

Now add each of these factors together:

1 + 6 = 7

2 + 3 = 5

-1 + -6 = -7

-2 + -3 = -5

Now compare this list to the coefficient of the linear term. In this case we have a 7. Thus we want to choose the 1, 6 pair. (Note: If no such pair exists, we cannot factor the trinomial.)

So:

Write the linear term as a sum using the pair we found above: 7x = 1x + 6x

Now factor what you can from the parenthesis. The first pair of terms has a common x and the second pair of terms has a common 2:

Now note that each term has a common 3x + 1. Factor this out to the right:

As a check you should always multiply this out:

-Dan