1. Faktor: $3\mathrm{\ne }03\backslash neq0$

2. Faktor: $x-\mathrm{1,5}=0\Rightarrow x=\mathrm{1,5}x-1\{,\}5=0\backslash ;\backslash Rightarrow\; \backslash ;x=1\{,\}5$

3. Faktor: $x+2=0\Rightarrow x=-2x+2=0\backslash ;\backslash Rightarrow\; \backslash ;x=-2$

Die Gleichung hat die Lösungsmenge: $\mathbb{L}=\{-2;\mathrm{1,5}\}\backslash mathbb\{L\}=\backslash \{-2;1\{,\}5\backslash \}$

1. Faktor: $3x-2=0\Rightarrow x={\displaystyle \frac{2}{3}}3x-2=0\backslash ;\backslash Rightarrow\; \backslash ;x=\backslash dfrac\{2\}\{3\}$

2. Faktor: ${\displaystyle \frac{1}{2}}x+4=0\Rightarrow x=-8\backslash dfrac\{1\}\{2\}x+4=0\backslash ;\backslash Rightarrow\; \backslash ;x=-8$

Die Gleichung hat die Lösungsmenge: $\mathbb{L}=\{-8;\frac{2}{3}\}\backslash mathbb\{L\}=\backslash \{-8;\backslash frac\{2\}\{3\}\backslash \}$

1. Faktor: $x+2=0\Rightarrow x=-2x+2=0\backslash ;\backslash Rightarrow\; \backslash ;x=-2$

2. Faktor: $x+2=0\Rightarrow x=-2x+2=0\backslash ;\backslash Rightarrow\; \backslash ;x=-2$

Die Gleichung hat eine doppelte Lösung $x_{\mathrm{1,2}}=-2x\_\{1\{,\}2\}=-2$ und damit die Lösungsmenge: $\mathbb{L}=\{-2\}\backslash mathbb\{L\}=\backslash \{-2\backslash \}$

1. Faktor: $4x-{\displaystyle \frac{2}{3}}=04x-\backslash dfrac\{2\}\{3\}=0$

2. Faktor: ${\displaystyle \frac{1}{3}}x+{\displaystyle \frac{1}{8}}=0\backslash dfrac\{1\}\{3\}x+\backslash dfrac\{1\}\{8\}=0$

Die Gleichung hat die Lösungsmenge: $\mathbb{L}=\{-{\displaystyle \frac{3}{8}};{\displaystyle \frac{1}{6}}\}\backslash mathbb\{L\}=\backslash \{-\backslash dfrac\{3\}\{8\};\backslash dfrac\{1\}\{6\}\backslash \}$