In the same way that you would solve equations because equivalent expressions are in effect equations
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It may be possible to solve equations. Expressions cannot be solved until they are converted, with additional information, into equations or inequalities which may have solutions.
There appears to be no equation in the question: only some disjoint expressions. Expressions cannot be solved.
In problems of motion, especially involving constant acceleration, a quadratic equation will from the formulas of motion to solve for time, usually. This is just one example.
To solve problems quickly you must have simple but effective method.
Convert all expressions to the same base.