To solve the polynomial equation c(x) = 2x^4 - x^3 - 26x^2 + 37x - 12 =0, we need to find the values of x that make the equation equal to zero.
The polynomial is of degree 4, therefore we know that it has four solutions (including complex numbers).
To find these solutions, we can use a method such as factoring, synthetic division, or the rational root theorem. In this case, we have found that the solutions are:
-4, 1/2, 1, and 3
So, we can write the solutions as:
x = -4, x = 1/2, x = 1, and x = 3.
These are the four values of x that make c(x) = 0, and are thus the solutions to this polynomial equation.