Verified answer

[tex]( {x}^{2} + 4x + 6) {}^{2} - 5( {x}^{2} +4 x + 6) = 6 \\ {x}^{2} + 4 x+ 6 = a \\ {a}^{2} - 5a = 6 \\ a {}^{2} - 5a - 6 = 0 \\ D = ( - 5) {}^{2} - 4 \times ( - 6) = 25 + 24 = 49 \\ a_{1} = \frac{5 + 7}{2} = \frac{12}{2} = 6\\ a_{2} = \frac{5 - 7}{2} = - \frac{2}{2} = - 1 \\ 1) \: \: a = 6 \\ {x}^{2} + 4x + 6 = 6 \\ {x}^{2} + 4x = 6 - 6 \\ {x}^{2} + 4x = 0 \\x (x + 4) = 0 \\ x_{1} = 0 \\ x_{2} = - 4 \\ 2) \: \: a = - 1 \\ {x}^{2} + 4x + 6 = - 1 \\ {x}^{2} + 4x + 7 = 0 \\D = {4}^{2} - 4 \times 7 = 16 - 28 = - 12\\ D < 0 \\ net \: \: \: korney[/tex]

Ответ: х = 0 ; х = - 4