Answer
$\{8,27\}$.
Work Step by Step
Substitute $x^{\frac{1}{3}}=A$ in the given equation.
$\Rightarrow A^2-5A+6=0$
Rewrite middle term $-5A$ as $-3A-2A$.
$\Rightarrow A^2-3A-2A+6=0$
Group terms.
$\Rightarrow (A^2-3A)+(-2A+6)=0$
Factor each term.
$\Rightarrow A(A-3)-2(A-3)=0$
Factor out $(A-3)$.
$\Rightarrow (A-3)(A-2)=0$
Set each factor equal to zero.
$\Rightarrow A-3=0$ or $A-2=0$
Isolate $A$.
$\Rightarrow A=3$ or $A=2$
Substitute back $A=x^{\frac{1}{3}}$
$\Rightarrow x^{\frac{1}{3}}=3$ or $x^{\frac{1}{3}}=2$
Cube both sides.
$\Rightarrow x=3^3$ or $x=2^3$
Simplify.
$\Rightarrow x=27$ or $x=8$
The solution set is $\{8,27\}$.
