Rearrange the terms of the quadratic expression into standard form ax² + bx + c.

The given expression is $2 + 5d - 12d^2$.
Rearranging it gives:

Let's factor directly by finding two numbers that multiply to $a \times c = (-12) \times 2 = -24$ and add up to $b = 5$.
The two numbers are 8 and $-3$.

Factor $4d$ from the first group and $-1$ from the second group:

To make the binomials identical, we can factor out $-4d$ from the first group instead:

This can also be written as $(2 - 3d)(4d + 1)$ by factoring out $-1$ from the first factor and $-1$ from the second factor, then multiplying the two $-1$s to get $+1$, or by factoring $-(12d^2 - 5d - 2)$.

Let's verify the factorization:
$(3d - 2)(-4d - 1) = 3d(-4d) + 3d(-1) - 2(-4d) - 2(-1)$
$= -12d^2 - 3d + 8d + 2$
$= -12d^2 + 5d + 2$
This matches the original expression.