Question 718982
<pre>
{{{matrix(2,1,"",

5z^(8/3)+4z^(5/3)-12z^(2/3)=0)}}}

Factor out the smallest power of z:

{{{matrix(2,1,"",

z^(2/3)(z^(6/3)+4z^(3/3)-12)=0)}}}

Reduce the fraction exponents in the parentheses:

{{{matrix(2,1,"",

z^(2/3)(z^2+4z^1-12)=0)}}}

Erase the 1 exponent:

{{{matrix(2,1,"",

z^(2/3)(z^2+4z-12)=0)}}}

Factor the parentheses:

{{{matrix(2,1,"",

z^(2/3)(z+2)(5z-6)=0)}}}

Use the zero-factor property

{{{matrix(2,1,"",

z^(2/3)=0)}}}     {{{matrix(2,1,"",

z+2=0)}}}     {{{matrix(2,1,"",

5z-6=0)}}}
{{{matrix(2,1,"",

     z=0)}}}         {{{matrix(2,1,"",

z=-2)}}}     {{{matrix(2,1,"",

5z=6)}}} 

                      {{{z=6/5}}}

Edwin</pre>