$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}} = {\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{3}}}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\mathtt{0}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1.5}}\\
{\mathtt{x}} = {\mathtt{0}}\\
\end{array} \right\}$$
Normal and cool
2x^3=3x^2 rewrite as
2x^3 - 3x^2 = 0 factor
x^2 (2x - 3) = 0 set both factors to 0.....and we have.....
x^2 = 0 and 2x - 3 = 0
take the square root of both sides add 3 to both sides
x = 0 2x = 3
divide both sides by 2
x = 3/2
So.....the two solutions are x = 0 aand x = 3/2
$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}} = {\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{3}}}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\mathtt{0}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1.5}}\\
{\mathtt{x}} = {\mathtt{0}}\\
\end{array} \right\}$$
Normal and cool