Final answer:
The solution to the equation -m^2 + 8m = 0 is found by factoring out an m and using the zero product property, yielding two solutions, m = 0 and m = 8. The correct answer is option (a).
Step-by-step explanation:
To find the solution for the equation -m^2 + 8m = 0, we can factor out an m from each term, since it is common to both terms. This gives us m(-m + 8) = 0. Now, according to the zero product property, we know that if a product of two factors equals zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for m separately.
m = 0 is the first solution since it's one of the factors. The second factor, -m + 8 = 0, can be solved by adding m to both sides to get m = 8 as the second solution. Therefore, the two values that solve the equation are m = 0 and m = 8.
The correct answer to the student's question, separating the values with a comma, is m = 0, m = 8, which corresponds to option (a).