+590 New Year, New Start, New Answer!
First answer of the year for me.
Alright, I'll try to explain this the best I can using a keyboard. 
The equation is x^2(6x - 11)(7x - 8) = 0
So, you have to figure out what you can put in for x for the whole thing to equal 0.
Roots mean possible solutions.
Let's "divide" the equation into 3 parts.
We know that anything multiplied by 0 is 0.
And 0 to the power of anything is still 0.
So if you plug in 0 for x^2(6x - 11)(7x - 8) = 0, You get 0 (it would look like "0(6x-11)(7x-8)" )
So the first root is 0.
Next, let's look at the (6x - 11) part.
Remember that anything multiplied by 0 is 0.
So, 6x - 11 must equal to 0.
6x-11=0
6x=11
x=11/6
So another root is 11/6.
Finally, let's look at (7x-8)
That should also equal 0, no matter what it is multiplied by.
7x-8=0
7x=8
x=8/7
The last root is 8/7
So the three roots are 0, 11/6, and 8/7.
