Quaternion or 3x3 Rotation Matrix Solver

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Is there a generalized formula or formulas be it that quaternion multiplication is not commutative, to solve for the equations:

Qa * X = Qb; solve for X

X * Qa = Qb; solve for X

where Qa is an arbitrary quaternion with Qb as a target quaternion?

Be it that quaternion multiplication and rotation matrix multiplication are supposed to be isomorphic as I've read, is there an equivalent equation for 3x3 rotation matrices?