1. **Problem:** Simplify the expression $2x(2x - 6) - 3x(x + 5)$. 2. **Formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to expand each term. 3. **Step-by-step work:** - Expand: $2x(2x) - 2x(6) - 3x(x) - 3x(5)$ - Simplify: $4x^2 - 12x - 3x^2 - 15x$ - Combine like terms: $(4x^2 - 3x^2) + (-12x - 15x) = x^2 - 27x$ 4. **Final answer:** $x^2 - 27x$