1. Stating the problem: Solve the equation $$3x + 32.1 = 5x - 0.3$$. 2. Write down the equation: $$3x + 32.1 = 5x - 0.3$$ 3. To isolate $x$, first move all terms involving $x$ to one side and constants to the other side. Subtract $3x$ from both sides: $$\cancel{3x} + 32.1 = 5x - 0.3 - \cancel{3x}$$ which simplifies to $$32.1 = 2x - 0.3$$ 4. Next, add $0.3$ to both sides to move constants to the left: $$32.1 + 0.3 = 2x - 0.3 + 0.3$$ which simplifies to $$32.4 = 2x$$ 5. Finally, divide both sides by 2 to solve for $x$: $$\frac{32.4}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to $$x = 16.2$$ 6. Therefore, the solution is: $$\boxed{16.2}$$