To find the x-intercepts of the function f(x) = -3x(x + 5), we set the function equal to zero: -3x(x + 5) = 0. According to the zero product property, if the product of two factors equals zero, at least one of the factors must be zero. This gives us two equations to solve: 1) x = 0 and 2) x + 5 = 0, which simplifies to x = -5. Therefore, the x-intercepts are the points where the graph of the function crosses the x-axis, which occur at x = 0 and x = -5.