1. **Problem statement:** Solve the equation $$ (6)(x-3)5x = 0 $$ for $x$. 2. **Formula and rules:** The product of factors equals zero if and only if at least one of the factors is zero. That is, if $$a \times b = 0$$ then either $$a=0$$ or $$b=0$$. 3. **Apply the zero product property:** The factors are $$6$$, $$(x-3)$$, and $$5x$$. Since $$6 \neq 0$$, we focus on: $$(x-3) = 0$$ or $$5x = 0$$. 4. **Solve each equation:** - For $$(x-3) = 0$$: $$x = 3$$ - For $$5x = 0$$: $$\cancel{5}x = 0 \Rightarrow x = 0$$ 5. **Final answer:** The solutions to the equation are $$x = 0$$ and $$x = 3$$. These are the values of $x$ that satisfy the original equation.