Solve by Factoring x^(2/3)-3x^(1/3)-18=0

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -18}$ and whose sum is ${\displaystyle -3}$.

Write the factored form using these integers.

Set ${\displaystyle x^{\frac{1}{3}}-6}$ equal to ${\displaystyle 0}$.

Solve ${\displaystyle x^{\frac{1}{3}}-6=0}$ for ${\displaystyle x}$.

Set ${\displaystyle x^{\frac{1}{3}}+3}$ equal to ${\displaystyle 0}$.

Solve ${\displaystyle x^{\frac{1}{3}}+3=0}$ for ${\displaystyle x}$.