Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.
Noether's Transformation Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 207, 1959.Referenced on Wolfram|Alpha
Noether's Transformation TheoremCite this as:
Weisstein, Eric W. "Noether's Transformation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NoethersTransformationTheorem.html