1. **State the problem:** We need to find the value of the expression $2x(x^2+5)+3$ when $x=2$. 2. **Write the expression:** $$2x(x^2+5)+3$$ 3. **Substitute $x=2$ into the expression:** $$2(2)((2)^2+5)+3$$ 4. **Calculate inside the parentheses:** $$(2)^2 = 4$$ So, $$(4 + 5) = 9$$ 5. **Multiply:** $$2 \times 2 \times 9 = 36$$ 6. **Add 3:** $$36 + 3 = 39$$ **Final answer:** The value of the expression when $x=2$ is **39**.