1. **State the problem:** Simplify the expression $x^2 - 2x + 3 + 2x^2 + 4x - 5$. 2. **Combine like terms:** Group the $x^2$ terms, the $x$ terms, and the constant terms separately. 3. **Add the $x^2$ terms:** $x^2 + 2x^2 = 3x^2$. 4. **Add the $x$ terms:** $-2x + 4x = 2x$. 5. **Add the constants:** $3 - 5 = -2$. 6. **Write the simplified expression:** $$3x^2 + 2x - 2$$. This is the simplified form of the given expression.