The substitution of
(1)

into the standard form cubic equation
(2)

The result reduces the cubic to the equation
(3)

which is easily turned into a quadratic equation in by multiplying through by to obtain
(4)

The substitution of
(1)

into the standard form cubic equation
(2)

The result reduces the cubic to the equation
(3)

which is easily turned into a quadratic equation in by multiplying through by to obtain
(4)

Weisstein, Eric W. "Vieta's Substitution." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/VietasSubstitution.html