How many solutions over the complex number system does this polynomial have? . 2x^4-3x^3-24x^2+13x+12=0

According to the Fundamental Theorem of Algebra on the Roots of Polynomials, the number of roots is equal to the degree of the polynomial. In this case, the polynomial is a fourth degree polynomial. Therefore, there are 4 solutions to the polynomial which over the complex number system.