Solve the equation. Express numbers in exact simplest form. \[ q^{3}+9 q=6 q^{2} \] The solution set is \( \{\square\} \). \( \square \square, \square, \ldots \frac{\square}{\square} \)

To solve the equation \( q^{3} + 9q = 6q^{2} \), we first rearrange all terms to one side: \[ q^{3} - 6q^{2} + 9q = 0 \] Next, we factor out \( q \): \[ q(q^{2} - 6q + 9) = 0 \] This gives us one solution: \[ q = 0 \] Next, we focus on the quadratic factor \( q^{2} - 6q + 9 \), which can be factored further: \[ q^{2} - 6q + 9 = (q - 3)(q - 3) = (q - 3)^{2} \] This gives us a double root: \[ q = 3 \] Thus, the complete solution set is \( \{0, 3\} \), where \( 3 \) is counted twice due to its multiplicity. Therefore, the solution set in exact simplest form is: \[ \{0, 3, 3\} \] So the fill-in looks like: The solution set is \( \{0, 3, 3\} \).