Solve -p(51+z)=dz+84

$$- p ( 51 + z ) = d z + 84$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=-\frac{pz+51p+84}{z}\text{, }&z\neq 0\\d\in \mathrm{C}\text{, }&z=0\text{ and }p=-\frac{28}{17}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -p by 51+z.

$$51\left(-p\right)+\left(-p\right)z=dz+84$$

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

$$dz+84=51\left(-p\right)+\left(-p\right)z$$

Subtract 84 from both sides.

$$dz=51\left(-p\right)+\left(-p\right)z-84$$

Multiply 51 and -1 to get -51.

$$dz=-51p-pz-84$$

The equation is in standard form.

$$zd=-pz-51p-84$$

Divide both sides by z.

$$\frac{zd}{z}=\frac{-pz-51p-84}{z}$$

Dividing by z undoes the multiplication by z.

$$d=\frac{-pz-51p-84}{z}$$

Divide -51p-pz-84 by z.

$$d=-\frac{pz+51p+84}{z}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{dz+84}{z+51}\text{, }&z\neq -51\\p\in \mathrm{C}\text{, }&d=\frac{28}{17}\text{ and }z=-51\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -p by 51+z.

$$51\left(-p\right)+\left(-p\right)z=dz+84$$

Multiply 51 and -1 to get -51.

$$-51p-pz=dz+84$$

Combine all terms containing p.

$$\left(-51-z\right)p=dz+84$$

The equation is in standard form.

$$\left(-z-51\right)p=dz+84$$

Divide both sides by -51-z.

$$\frac{\left(-z-51\right)p}{-z-51}=\frac{dz+84}{-z-51}$$

Dividing by -51-z undoes the multiplication by -51-z.

$$p=\frac{dz+84}{-z-51}$$

Divide dz+84 by -51-z.

$$p=-\frac{dz+84}{z+51}$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{pz+51p+84}{z}\text{, }&z\neq 0\\d\in \mathrm{R}\text{, }&z=0\text{ and }p=-\frac{28}{17}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -p by 51+z.

$$51\left(-p\right)+\left(-p\right)z=dz+84$$

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

$$dz+84=51\left(-p\right)+\left(-p\right)z$$

Subtract 84 from both sides.

$$dz=51\left(-p\right)+\left(-p\right)z-84$$

Multiply 51 and -1 to get -51.

$$dz=-51p-pz-84$$

The equation is in standard form.

$$zd=-pz-51p-84$$

Divide both sides by z.

$$\frac{zd}{z}=\frac{-pz-51p-84}{z}$$

Dividing by z undoes the multiplication by z.

$$d=\frac{-pz-51p-84}{z}$$

Divide -51p-pz-84 by z.

$$d=-\frac{pz+51p+84}{z}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{dz+84}{z+51}\text{, }&z\neq -51\\p\in \mathrm{R}\text{, }&d=\frac{28}{17}\text{ and }z=-51\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -p by 51+z.

$$51\left(-p\right)+\left(-p\right)z=dz+84$$

Multiply 51 and -1 to get -51.

$$-51p-pz=dz+84$$

Combine all terms containing p.

$$\left(-51-z\right)p=dz+84$$

The equation is in standard form.

$$\left(-z-51\right)p=dz+84$$

Divide both sides by -z-51.

$$\frac{\left(-z-51\right)p}{-z-51}=\frac{dz+84}{-z-51}$$

Dividing by -z-51 undoes the multiplication by -z-51.

$$p=\frac{dz+84}{-z-51}$$

Divide dz+84 by -z-51.

$$p=-\frac{dz+84}{z+51}$$