1. **State the problem:** Simplify the expression $$\frac{20x^2 + 8x}{5x + 2}$$. 2. **Identify the formula and rules:** We want to simplify a rational expression by factoring the numerator and denominator and canceling common factors. 3. **Factor the numerator:** $$20x^2 + 8x = 4x(5x + 2)$$ 4. **Rewrite the expression:** $$\frac{4x(5x + 2)}{5x + 2}$$ 5. **Cancel the common factor:** $$\frac{4x\cancel{(5x + 2)}}{\cancel{5x + 2}} = 4x$$ 6. **Final answer:** $$4x$$ This simplification is valid as long as $$5x + 2 \neq 0$$, i.e., $$x \neq -\frac{2}{5}$$ to avoid division by zero.