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For example:

Find the roots of x^2-4x+3=0

Suppose we have no knowledge of the algebraic techniques for solving this equation. Had we wished to write the solution set for this equation using the set builder method

S={x: x^2-4x+3=0}

I feel like we are being redundant. We are introducing new expressions to express the same thing. Yes the implicit form tells us what property members have in common to be part of the solution set (this is understood from the problem had we not used sets). But the task of finding the members themselves namely the implicit form of the solution set still requires us to discover techniques like factoring and the quadratic equation.