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The error in the student's work is in the distribution step when simplifying "m(2m+5)-6(2m+5)=0." The student should have distributed the -6 to both terms inside the parentheses. The correct distribution should look like this: "m(2m+5) - 6(2m+5) = 0" becomes "2m^2 + 5m - 12m - 30 = 0."
Therefore, the correct factorization should be "(2m + 5)(m - 6) = 0." The correct answers are m = -5/2 and m = 6.