-x(3x+2)^2=-(x-1)(3x+2)

Lösung

- x (3 x + 2)^{2} = - (x - 1) (3 x + 2)

x = - \frac{2}{3}, x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

Schritte zur Lösung

- x (3 x + 2)^{2} = - (x - 1) (3 x + 2)

Verschiebe

(x - 1) (3 x + 2)

auf die linke Seite

- x (3 x + 2)^{2} + (x - 1) (3 x + 2) = 0

Faktorisiere

- x (3 x + 2)^{2} + (x - 1) (3 x + 2) : - (3 x + 2) (3 x^{2} + x + 1)

- (3 x + 2) (3 x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x + 2 = 0 or 3 x^{2} + x + 1 = 0

Löse

3 x + 2 = 0 : x = - \frac{2}{3}

Löse

3 x^{2} + x + 1 = 0 : x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

Die Lösungen sind

x = - \frac{2}{3}, x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

(x - 3) (x^{2} - 4 x + 4) = 0

x^{3} + 5 x - 7 = 0

x^{3} - 6 x^{2} + 8 x = x^{2} - 4 x

x^{2} (x + 1) + 4 (x + 1) = 0

2 x^{3} + 46 = 100