To solve the equation \( x^2(x - 1) + 4(x - 1) = 0 \), we can start by factoring it.

Notice that both terms share a common factor of \( (x - 1) \). We can factor it out:

\[
(x - 1)(x^2 + 4) = 0
\]

Now, we can set each factor equal to zero:

1. \( x - 1 = 0 \)
2. \( x^2 + 4 = 0 \)

**Solving the first equation:**

\[
x - 1 = 0 \implies x = 1
\]

**Solving the second equation:**

\[
x^2 + 4 = 0 \implies x^2 = -4
\]

This gives us:

\[
x = \pm 2i
\]

**Final Solutions:**

The complete set of solutions to the equation \( x^2(x - 1) + 4(x - 1) = 0 \) is:

\[
x = 1, \quad x = 2i, \quad x = -2i
\]