Question 548757
Hi, i'm a sophomore and I recently just went over this section.

First step is to subtract 27m and add 9 to both sides of the equation.

{{{12m^3-4m^2-27m+9=0}}}

Now you group them and root out the greatest common factor from both groups as so and a note, the two other problems in parentheses have to  be the same. In this problem those two are (3m-1)

{{{4m^2(3m-1)-9(3m-1)}}}

now, you have to combine the two group and 4m^2 -9 as so.

{{{(4m^2-9)(3m-1)}}}

now, you can factor 4m^2-9 again for your other solutions. You can plug in 0x to put it in {{{ax^2+bx+c}}} form. Or you can plug it into quadratic formula. I am going to plug it into quadratic formula. {{{4m^2}}} being A, 0 being B, and -9 being C.

{{{x=-0+-sqrt(0^2-4(4)(-9))/2(4)}}}

Now,simplify the quadratic formula to get 2 of your solutions.

So your 3 solutions would be {{{-3/2}}}, {{{3/2}}}, and {{{1/3}}}, (the one third from (3m-1)).