Solve xi(a+3)x^10-2+6=0

$$\xi ( a + 3 ) x ^ { 10 - 2 } + 6 = 0$$

Solve for a

$$a=-3-\frac{6}{\xi x^{8}}$$

$$x\neq 0\text{ and }\xi \neq 0$$

Steps for Solving Linear Equation

Subtract 2 from 10 to get 8.

$$\xi \left(a+3\right)x^{8}+6=0$$

Use the distributive property to multiply \xi by a+3.

$$\left(\xi a+3\xi \right)x^{8}+6=0$$

Use the distributive property to multiply \xi a+3\xi by x^{8}.

$$\xi ax^{8}+3\xi x^{8}+6=0$$

Subtract 3\xi x^{8} from both sides. Anything subtracted from zero gives its negation.

$$\xi ax^{8}+6=-3\xi x^{8}$$

Subtract 6 from both sides.

$$\xi ax^{8}=-3\xi x^{8}-6$$

The equation is in standard form.

$$\xi x^{8}a=-3\xi x^{8}-6$$

Divide both sides by \xi x^{8}.

$$\frac{\xi x^{8}a}{\xi x^{8}}=\frac{-3\xi x^{8}-6}{\xi x^{8}}$$

Dividing by \xi x^{8} undoes the multiplication by \xi x^{8}.

$$a=\frac{-3\xi x^{8}-6}{\xi x^{8}}$$

Divide -3\xi x^{8}-6 by \xi x^{8}.

$$a=-3-\frac{6}{\xi x^{8}}$$

Solve for x (complex solution)

$$x\in \sqrt[8]{6}e^{\frac{3\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{5\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{7\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{9\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{11\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{13\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}},\sqrt[8]{6}e^{\frac{15\pi i}{8}}\xi ^{-\frac{1}{8}}\left(a+3\right)^{-\frac{1}{8}}$$

$$a\neq -3\text{ and }\xi \neq 0$$

Solve for x

$$x=\sqrt[8]{-\frac{6}{\xi \left(a+3\right)}}$$

$$x=-\sqrt[8]{-\frac{6}{\xi \left(a+3\right)}}\text{, }\left(\xi >0\text{ and }a<-3\right)\text{ or }\left(a>-3\text{ and }\xi <0\right)$$