To solve the inequality

\[
2x - x(3x + 1) \leq 21 - 3x(x + 2),
\]

let's simplify each side step by step.

1. **Distribute** on both sides:

Left side:
\[
2x - x(3x + 1) = 2x - (3x^2 + x) = 2x - 3x^2 - x = -3x^2 + x.
\]

Right side:
\[
21 - 3x(x + 2) = 21 - (3x^2 + 6x) = 21 - 3x^2 - 6x.
\]

2. **Combine terms** on each side:
\[
-3x^2 + x \leq 21 - 3x^2 - 6x.
\]

3. **Add \(3x^2\)** to both sides:
\[
x \leq 21 - 6x.
\]

4. **Add \(6x\)** to both sides:
\[
7x \leq 21.
\]

5. **Divide by 7**:
\[
x \leq 3.
\]

Thus, the solution to the inequality is

\[
x \leq 3.
\]

This means \(x\) can be any value less than or equal to 3.