Solve 0=b+xb+z^x

$$0 = b + x b + z ^ { x }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{z^{x}}{x+1}\text{, }&x\neq -1\\b\in \mathrm{C}\text{, }&x=-1\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$b+xb+z^{x}=0$$

Subtract z^{x} from both sides. Anything subtracted from zero gives its negation.

$$b+xb=-z^{x}$$

Combine all terms containing b.

$$\left(1+x\right)b=-z^{x}$$

The equation is in standard form.

$$\left(x+1\right)b=-z^{x}$$

Divide both sides by 1+x.

$$\frac{\left(x+1\right)b}{x+1}=-\frac{z^{x}}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

$$b=-\frac{z^{x}}{x+1}$$

Solve for b

$$b=-\frac{z^{x}}{x+1}$$

$$\left(x\neq -1\text{ and }z>0\right)\text{ or }\left(z=0\text{ and }x>0\right)\text{ or }\left(x\neq -1\text{ and }z<0\text{ and }Denominator(x)\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$b+xb+z^{x}=0$$

Subtract z^{x} from both sides. Anything subtracted from zero gives its negation.

$$b+xb=-z^{x}$$

Combine all terms containing b.

$$\left(1+x\right)b=-z^{x}$$

The equation is in standard form.

$$\left(x+1\right)b=-z^{x}$$

Divide both sides by 1+x.

$$\frac{\left(x+1\right)b}{x+1}=-\frac{z^{x}}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

$$b=-\frac{z^{x}}{x+1}$$