Solve for x in the given inequality: $\displaystyle 6x - x^2 \ge\;9$

My Work:

$\displaystyle -x^2 + 6x - 9 \ge\; 0$

$\displaystyle (-x + 3)(x - 3) \ge\; 0$

$\displaystyle -x + 3\ge\; 0\Longrightarrow -x \ge\; -3\Longrightarrow x\le\; 3$

$\displaystyle x - 3 \ge\; 0\Longrightarrow x \ge\; 3$

What did I do wrong?