It simply states that every polynomial equation of degree "n" with complex coefficients has "n" roots in the complex numbers.  
When Cardano applied it to the formula, "x cubed equals 15x plus 4," it gave an answer involving the square root of  "negative 121," but he knew the equation had "x equals 4" as a solution, so he showed that it could work with quantities more general than real numbers.  A false proof it was given by Leibniz when he asserted that "x to the fourth plus t to the fourth" could not be written as a product of two real quadratic factors, but he didn't notice that the square root of "i"could be written in the form "a plus (b times i)."   It simply states that every polynomial equation of degree "n" with complex coefficients has "n" roots in the complex numbers.  FTP, name this basic theorem of mathematics.
When Cardano applied it to the formula, "x cubed equals 15x plus 4," it gave an answer involving the square root of  "negative 121," but he knew the equation had "x equals 4" as a solution, so he showed that it could work with quantities more general than real numbers.  
Fundamental Theorem of Algebra