1. **State the problem:** Given that $3+2i$ is a root of a polynomial equation with real coefficients, find the other root(s). 2. **Important rule:** For polynomials with real coefficients, complex roots always come in conjugate pairs. This means if $3+2i$ is a root, then its conjugate $3-2i$ must also be a root. 3. **Explanation:** The conjugate of a complex number $a+bi$ is $a-bi$. Since the coefficients are real, the polynomial must have $3-2i$ as a root to ensure the polynomial remains with real coefficients. 4. **Conclusion:** The other root corresponding to $3+2i$ is $3-2i$. **Final answer:** The other root is $3-2i$.