Find the solutions to the equation. begin equation . . 3 times, x raised to the second power, minus 2 times x, minus 5 . . equals 0 . . end equation

You can write the equation using conventional symbols as
3x^2 - 2x - 5 = 0

You can recognize that the middle coefficient is equal to the sum of the other two, so those two coefficients can be used to factor the equation.
  (1/3)(3x +3)(3x -5) = 0 . . . . . put the coefficients in the form (1/a)(ax + ...)(ax + ...)  (x+1)(3x-5) = 0 . . . . . simplify

The solutions are the values of x that make one or the other of the factors equal to zero.
  x = -1
  x = 5/3

The correct one is c.