Answer:
[tex]m=0,3,5[/tex]
Explanation:
We were given the equation:
[tex]5m^3-40m^2+75m=0[/tex]
We are to solve it as shown below:
[tex]\begin{gathered} 5m^{3}-40m^{2}+75m=0 \\ \text{Let's factor the equation into a simpler form, we have} \\ m(5m^2-40m+75)=0 \\ m=0 \\ 5m^2-40m+75=0 \\ \text{Simplifying this equation by dividing through by ''5'', we have:} \\ m^2-8m+15=0 \\ \text{Factorising, we have:} \\ m^2-5m-3m+15=0 \\ m(m-5)-3(m-5)=0 \\ (m-3)(m-5)=0 \\ \Rightarrow m-3=0,m-5=0 \\ m=3,m=5 \\ \\ \therefore m=0,3,5 \end{gathered}[/tex]
Therefore, m equals 0, 3, 53
