1. **State the problem:** We have the equation $$6x^2(3x - 16)(3x - u) = 0$$ and the sum of all solutions (roots) is 13. We need to find the value of $u$. 2. **Understand the roots:** The roots come from each factor set to zero: - From $6x^2 = 0$, roots are $x=0$ (with multiplicity 2). - From $3x - 16 = 0$, root is $x=\frac{16}{3}$. - From $3x - u = 0$, root is $x=\frac{u}{3}$. 3. **Sum of roots:** The total sum of roots, counting multiplicity, is: $$0 + 0 + \frac{16}{3} + \frac{u}{3} = 13$$ 4. **Set up the equation:** $$\frac{16}{3} + \frac{u}{3} = 13$$ 5. **Multiply both sides by 3 to clear denominators:** $$3 \times \left(\frac{16}{3} + \frac{u}{3}\right) = 3 \times 13$$ $$\cancel{3} \times \left(\frac{16}{\cancel{3}} + \frac{u}{\cancel{3}}\right) = 39$$ $$16 + u = 39$$ 6. **Solve for $u$:** $$u = 39 - 16$$ $$u = 23$$ **Final answer:** The value of $u$ is $23$.