The present disclosure provides substituted isoxazole carboxamide compounds having Formula (I) and the pharmaceutically acceptable salts and solvates thereof, wherein R1, R2, A, X, and Z are defined as set forth in the specification. The present disclosure is also directed to the use of compounds of Formula I to treat a disorder responsive to the blockade of SMYD proteins such as SMYD3 or SMYD2. Compounds of the present disclosure are especially useful for treating cancer.