Olympiad Mathematics | The three solutions | Russian | Can you solve this one?

To solve the equation 2m³ = (m-2)³, rearrange it to (m-2)³ - (2m)³ = 0 and apply the difference of cubes identity a³ - b³ = (a-b)(a² + ab + b²), where a = m-2 and b = 2m. This yields (m-2-2m)((m-2)² + (m-2)(2m) + (2m)²) = 0, which simplifies to (m+2)(7m² - 8m + 4) = 0. The first solution is m = -2, and the quadratic factor 7m² - 8m + 4 = 0 gives complex solutions m = (4 ± 2i√3)/7 using the quadratic formula.