The thermal decomposition of siderite is interesting aspect. First, the answer to your question is your textbook has mistakenly put a common factor (of 2) to balance the chemical equation. It is not wrong but traditionally we do not put a common factor on equations, unless we intended to add or subtract two of more equations. Said that, I have a doubt that this equation is correct at all, based on literature. Although this must have been too much for the OP, I'd like to make my point.
One such publication reveals the following (Ref.1):
Abstract: In order to provide a better theoretical foundation for utilisation of Xinjiang siderite resources in China, its thermal decomposition behaviour was studied in neutral and oxidising atmospheres by employing thermodynamics analysis, chemical titration, thermogravimetric, and X-ray diffraction means. Isothermal experiments were conducted to investigate the thermal decomposition kinetics of siderite lump in a weakly oxidising atmosphere at $\pu{500–850 ^\circ C}$. The results reveal that siderite has self-magnetisation characteristics under controlled conditions, and the phase evolution process and final products of decomposition depend temperature and atmosphere. The phase transformation process in weak oxidising atmosphere follows the steps as: $\ce{FeCO3 -> Fe3O4 -> \gamma-Fe2O3}$ at $\pu{550 ^\circ C}$, and $\ce{FeCO3 -> FeO + Fe3O4 -> Fe3O4 -> \gamma-Fe2O3 -> \alpha-Fe2O3}$ at $\pu{800 ^\circ C}$. In inert atmosphere, the decomposition pathway is $\ce{FeCO3 -> Fe3O4}$ below $\pu{733 ^\circ C}$ and $\ce{FeCO3 -> FeO + Fe3O4}$ above $\pu{733 ^\circ C}$. The molar ratio of $\ce{FeO/Fe3O4}$ increases with temperature. The decomposition kinetics of siderite lump in oxygen-deficient atmosphere is consistent with chemical reaction control in the temperature range $\pu{500–700 ^\circ C}$ and nucleation and growth mechanism in the $\pu{750–850 ^\circ C}$. The corresponding activation energies are $53.73$ and $\pu{38.15 KJ mol−1}$, respectively.
It is clear from this reference that decomposition products of siderite ($\ce{FeCO3}$) are dependent on the temperature. Yet, the authors have not obtained iron(II) oxide ($\ce{FeO}$) as a sole product. Another recent publication (Ref.2) claimed $\ce{Fe2O3}$ as the final product when $\ce{FeCO3}$ is heated above $\pu{400 ^\circ C}$, based on its thermal decomposition studies in air by DTA-TGA, XRD, SEM, and Mossbauer measurements. The authors have observed a weight loss of about $32 \%$ at the single exothermic peak at $\pu{495 ^\circ C}$. They claimed the theoretical weight loss is $31.1 \%$, thus decomposition should be consistent with the equation:
$$\ce{2FeCO3 -> Fe2O3 + CO + CO2}$$
This finding is also consistent with an old Science publication claiming $\ce{FeCO3}$ decomposed to magnetite ($\ce{Fe3O4}$) and graphite when heating in equilibration with graphite at $\pu{455–465 ^\circ C}$ (Ref.3).
All these evidence directed to doubt the simple equation given in OP's textbook.
References:
- Y. H. Luo, D. Q. Zhu, J. Pan, X. L. Zhou, “Thermal decomposition behaviour and kinetics of Xinjiang siderite ore,” Mineral Processing and Extractive Metallurgy - Transactions of the Institutions of Mining and Metallurgy: Section C 2016, 125(1), 17-25 (https://doi.org/10.1080/03719553.2015.1118213).
- A. A. El-Bellihi, “Kinetics of Thermal Decomposition of Iron Carbonate,” Egypt. J. Chem. 2010, 53(6), 871-884 (DOI: 10.21608/EJCHEM.2010.1268).
- Bevan M. French1, P. E. Rosenberg, “Siderite ($\ce{FeCO3}$): Thermal Decomposition in Equilibrium with Graphite,” Science 1965, 147(3663), 1283-1284 (DOI: 10.1126/science.147.3663.1283).