Is { x : x2 - 5x - 6 = 0 } = {2, 3} ?
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x2 - 5x - 6 = 0
⇒ x2 - 6x + x - 6 = 0
⇒ (x2 - 6x) + (x - 6) = 0
⇒ x(x - 6) + 1(x - 6) = 0
⇒ (x - 6)(x + 1) = 0
⇒ (x - 6) = 0 or (x + 1) = 0
⇒ x = 6 or x = -1
Hence, { x : x2 - 5x - 6 = 0 } ≠ { 2, 3 }.
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