SOLUTION: How do I solve this? 12m^3-4m^2 = 27m-9, my teacher said that since it is to the 3rd power I need three answers

Algebra ->  Exponents -> SOLUTION: How do I solve this? 12m^3-4m^2 = 27m-9, my teacher said that since it is to the 3rd power I need three answers      Log On


   

Question 548757: How do I solve this? 12m^3-4m^2 = 27m-9, my teacher said that since it is to the 3rd power I need three answers
Answer by Hsj7339(2) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E3-4m%5E2-27m%2B9=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%5E2%283m-1%29-9%283m-1%29
now, you have to combine the two group and 4m^2 -9 as so.
%284m%5E2-9%29%283m-1%29
now, you can factor 4m^2-9 again for your other solutions. You can plug in 0x to put it in ax%5E2%2Bbx%2Bc form. Or you can plug it into quadratic formula. I am going to plug it into quadratic formula. 4m%5E2 being A, 0 being B, and -9 being C.
x=-0%2B-sqrt%280%5E2-4%284%29%28-9%29%29%2F2%284%29
Now,simplify the quadratic formula to get 2 of your solutions.
So your 3 solutions would be -3%2F2, 3%2F2, and 1%2F3, (the one third from (3m-1)).