Algebra · Polynomial equations · Factoring quadratics · Common factors · Difference of cubes
Find every real number \(x\) for which
\[ \left(2x^{2} + 7x + 6\right)^{3} - \left(x^{2} + 3x + 2\right)^{3} = \left(x^{2} + 4x + 4\right)\left(117x^{2} + 128x + 52\right) . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2025, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source