Question 73774
{{{x^(12/5) + 5x^(7/5) + 6x^(2/5) = 0}}}
{{{x^(2/5)(x^2 + 5x + 6) = 0}}}


As product of two quantities = 0, so at least one is zero.
Either {{{(x^2 + 5x + 6) = 0}}} or {{{x^(2/5)= 0}}}
i.e. {{{(x+2)(x+3) = 0}}} or {{{x = 0}}}
i.e. {{{(x+2)=0}}} or {{{(x+3) = 0}}} or {{{x = 0}}}
i.e. {{{x=-2}}} or {{{x=-3}}} or {{{x = 0}}}


Thus, the full set of solutions is x = 0, -2, -3.