Решите уравнения. разложив на множители.

(x+4) x = (x²+2x-8) (x+3)

x²+4x = x³+2x²-8x+3x²+6x-24

x²+4x = x³ + 5x² - 2x-24

x³+5x²-2x-24-x²-4x=0

x³+4x²-6x-24 = 0

x² (x+4) - 6 (x+4) = 0

(x+4) (x²-6) = 0

(x+4) (x-√6) (x+√6) = 0

x+4=0

x₁=-4

x-√6=0

x₂ = √6

x+√6=0

x₃=-√6

x (x²-x-6) = x²-9

x³-x²-6x=x²-9

x³-x²-6x-x²+9 = 0

x³-2x²-6x+9=0

x³+x²-3x - 3x²-3x+9=0

x (x²+x-3) - 3 (x²+x-3) = 0

(x-3) (x²+x-3) = 0

x-3=0

x₁=3

x²+x-3=0

D = 1²-4*1 * (-3) = 1+12=13

x₂ = (-1-√13) / (2*1) = (-1-√13) / 2

x₃ = (-1+√13) / 2