1. **State the problem:** Solve the equation $$\frac{15(x - 3)}{5} = 3(2x - 3)$$. 2. **Write down the formula and rules:** To solve linear equations, we simplify both sides and isolate the variable $x$. 3. **Simplify the left side:** $$\frac{15(x - 3)}{5} = 3(x - 3)$$ because $\frac{15}{5} = 3$. 4. **Rewrite the equation:** $$3(x - 3) = 3(2x - 3)$$. 5. **Expand both sides:** $$3x - 9 = 6x - 9$$. 6. **Bring all terms involving $x$ to one side and constants to the other:** Subtract $3x$ from both sides: $$\cancel{3x} - 9 = 6x - 9 - \cancel{3x}$$ which simplifies to $$-9 = 3x - 9$$. 7. **Add 9 to both sides:** $$-9 + 9 = 3x - 9 + 9$$ which simplifies to $$0 = 3x$$. 8. **Divide both sides by 3:** $$\frac{0}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ which simplifies to $$0 = x$$. 9. **Final answer:** $$x = 0$$. This equation has one solution.