SOLUTION: Can you please help me solve this? I'm supposed to solve for all roots but I'm not sure how. {{{8x^3+27=0}}}

You must learn the principle of factoring the sum and difference of
two cubes:

 

factors as



and

 

factors as



------------------------------

Your problem is the first case as it has a + sign between
the two terms:



Notice that  can be written as 

Notice that  can be written as 

So we write it as 



So  and 

and since

 

factors as



we factor the left side of 



as



Simplifying inside the second parentheses:





So we use the zero factor property:

,  

Solving the first,





So one root is  

Solving the second:



That doesn't factor so we resort to the
quadratic formula:

 

where , , 

 

 









Make two fractions on the right



Reduce the fractions by dividing top and 
bottom by 2:



So the other two roots are



and 



Edwin