2x^3=3x^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

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