If a value "satisfies a cubic equation" means that when you plug that value to the cubic, you get a true equation. So let's do that now.

\(\displaystyle (1 + 4i)^3 + 5(1+ 4i)^2 + k(1 + 4i) + m = 0\)

This should be easy enough for you to solve for *m* in terms of *k*, arriving at:

\(\displaystyle m = \text {(Real part as a function of k)} + i \text {(Imaginary part as a function of k)}\)

The problem text tells you that both *m* and *k* must be real, so what can you conclude about the imaginary part of *m*? What does that tell you about the value of *k*? What does that, then, tell you about the value of *m*?