Solve the equation by factoring81m^3-81m^2-36m+36=0

The solution set is {1, -2/3, 2/3}.

Step-by-step explanation:

81m^3-81m^2-36m+36=0

9(9m^3 - 9m^2 - 4m + 4) = 0

Looks  like 1 might be  one root:

f(1) = = 9*1 - 9*1 - 4*1  + 4 = 0  so one factor is (x - 1).

Divide the function  by x - 1:

        9m^2 - 4  <Quotient

m - 1 ) 9m^3 - 9m^2  - 4m + 4

         9m^3-9m^2

                       -4m + 4

                        -4m + 2

Now :

9m^2 - 4 = (3m - 2)(3m + 2).

so  m - 1 = 0  or 3m - 2 = 0 or 3m + 2 = 0

m = 1 , 2/3,  -2/3.