Solve 16z+29z=pz-v

$$16 z + 29 z = p z - v$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{v}{z}+45\text{, }&z\neq 0\\p\in \mathrm{C}\text{, }&z=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 16z and 29z to get 45z.

$$45z=pz-v$$

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

$$pz-v=45z$$

Add v to both sides.

$$pz=45z+v$$

The equation is in standard form.

$$zp=45z+v$$

Divide both sides by z.

$$\frac{zp}{z}=\frac{45z+v}{z}$$

Dividing by z undoes the multiplication by z.

$$p=\frac{45z+v}{z}$$

Divide 45z+v by z.

$$p=\frac{v}{z}+45$$

Solve for p

$$\left\{\begin{matrix}p=\frac{v}{z}+45\text{, }&z\neq 0\\p\in \mathrm{R}\text{, }&z=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 16z and 29z to get 45z.

$$45z=pz-v$$

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

$$pz-v=45z$$

Add v to both sides.

$$pz=45z+v$$

The equation is in standard form.

$$zp=45z+v$$

Divide both sides by z.

$$\frac{zp}{z}=\frac{45z+v}{z}$$

Dividing by z undoes the multiplication by z.

$$p=\frac{45z+v}{z}$$

Divide 45z+v by z.

$$p=\frac{v}{z}+45$$

Solve for v

$$v=z\left(p-45\right)$$

Steps for Solving Linear Equation

Combine 16z and 29z to get 45z.

$$45z=pz-v$$

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

$$pz-v=45z$$

Subtract pz from both sides.

$$-v=45z-pz$$

Divide both sides by -1.

$$\frac{-v}{-1}=\frac{z\left(45-p\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$v=\frac{z\left(45-p\right)}{-1}$$

Divide z\left(45-p\right) by -1.

$$v=pz-45z$$