find and explain the error in the students work below
solve: 2m^2-7m-30=0
2m^2+5m-12m-30=0
m(2m+5)-6(2m+5)=0
(2m+5)(m-6)=0
the student states that the answers are 2m+5 and m-6
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.