3d^{2}+23d+14

3d^{2}+23d+14

We can start with one of the factors to have a coefficient of 3 on the variable d and the other coefficient to be one because of the coefficient on d^{2}.

(3d+?)(d+?)

We know the ?'s have to multiply to 14, so we can try 1 and 14 or 2 and 7. We see that when we use 2 and 7 in the following manner, when multiplied and added, we obtain the expected coefficient of d, 23, in the original expression.

(3d+7)(d+2)