The equation wx^2 + w = 0 can be factored by taking out the common factor of w. This gives:
w(x^2 + 1) = 0
To solve for x, we need to find the values of x that make the equation true. Since w is a positive integer, the only way for the equation to be true is if x^2 + 1 = 0. However, there are no real numbers that satisfy this equation.
Therefore, the solution to the equation wx^2 + w = 0, where w is a positive integer, is that there are no real solutions.