The expression you've provided is a quadratic expression: \( 2x^2 + 2x + 3 \).

If you need to solve it, there are different methods depending on what you're trying to achieve. Let me know if you want to solve it for \( x \), factorize it, or analyze its properties.

### Would you like to:
1. Solve the quadratic equation \( 2x^2 + 2x + 3 = 0 \)?
2. Factorize the quadratic expression \( 2x^2 + 2x + 3 \)?
3. Complete the square for the expression \( 2x^2 + 2x + 3 \)?
4. Find the vertex of the parabola described by \( y = 2x^2 + 2x + 3 \)?
5. Determine the axis of symmetry for the parabola \( y = 2x^2 + 2x + 3 \)?
6. Calculate the discriminant of the quadratic equation \( 2x^2 + 2x + 3 = 0 \)?
7. Discuss the nature of the roots of the quadratic equation \( 2x^2 + 2x + 3 = 0 \)?
8. Graph the quadratic function \( y = 2x^2 + 2x + 3 \)?

**Tip:** The discriminant of a quadratic equation helps determine the nature of its roots (real vs. complex).

Learn how to solve the quadratic equation 2x^2 + 2x + 3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula and the quadratic formula theorem. Suitable for students in Grades 10-12.

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