Answer:
The equation 2x^2 + 6m = 2mx can be rearranged to 2x^2 - 2mx + 6m = 0. This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = -2m, and c = 6m.
For a quadratic equation to have no real solutions, its discriminant must be less than zero. The discriminant is given by the formula b^2 - 4ac. Substituting the values of a, b, and c into this formula, we get:
(-2m)^2 - 4(2)(6m) < 0
Solving this inequality for m, we find that the equation 2x^2 + 6m = 2mx has no real solutions when m < 0 or when m > 3.
So, for the value of m less than zero or greater than three, the equation has no real solutions.