Question 143674
You have the correct general idea, but a slightly different substitution makes this much easier to handle.


Let {{{u=root(3,(t+4))}}}


Substituting:


{{{u^2+7u+12=0}}}


Factoring:


{{{(u + 3)(u + 4)=0}}}


So:


{{{u=-3}}} or {{{u =-4}}}


Substituting back:


{{{root(3,(t+4))=-3}}}
{{{t+4=(-3)^3}}}
{{{t+4=-27}}}
{{{t=-31}}}


or:


{{{root(3,(t+4))=-4}}}
{{{t+4=(-4)^3}}}
{{{t+4=-64}}}
{{{t=-68}}}