1. **State the problem:** Expand and simplify the expression $x(4x - 2) + x(5x + 6)$. 2. **Use the distributive property:** Multiply $x$ by each term inside the parentheses. $$x(4x - 2) = x \cdot 4x - x \cdot 2 = 4x^2 - 2x$$ $$x(5x + 6) = x \cdot 5x + x \cdot 6 = 5x^2 + 6x$$ 3. **Combine the results:** $$4x^2 - 2x + 5x^2 + 6x$$ 4. **Group like terms:** $$ (4x^2 + 5x^2) + (-2x + 6x)$$ 5. **Simplify each group:** $$9x^2 + 4x$$ 6. **Final answer:** $$9x^2 + 4x$$