Solve -p(d+z)=-2z+59

$$- p ( d + z ) = - 2 z + 59$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{pz-2z+59}{p}\text{, }&p\neq 0\\d\in \mathrm{R}\text{, }&z=\frac{59}{2}\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-p\right)d+\left(-p\right)z=-2z+59$$

Subtract \left(-p\right)z from both sides.

$$\left(-p\right)d=-2z+59-\left(-p\right)z$$

Multiply -1 and -1 to get 1.

$$-pd=-2z+59+pz$$

The equation is in standard form.

$$\left(-p\right)d=pz-2z+59$$

Divide both sides by -p.

$$\frac{\left(-p\right)d}{-p}=\frac{pz-2z+59}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$d=\frac{pz-2z+59}{-p}$$

Divide zp-2z+59 by -p.

$$d=-\frac{pz-2z+59}{p}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{2z-59}{z+d}\text{, }&d\neq -z\\p\in \mathrm{R}\text{, }&z=\frac{59}{2}\text{ and }d=-\frac{59}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-p\right)d+\left(-p\right)z=-2z+59$$

Reorder the terms.

$$-pz-dp=-2z+59$$

Combine all terms containing p.

$$\left(-z-d\right)p=-2z+59$$

The equation is in standard form.

$$\left(-z-d\right)p=59-2z$$

Divide both sides by -z-d.

$$\frac{\left(-z-d\right)p}{-z-d}=\frac{59-2z}{-z-d}$$

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

$$p=\frac{59-2z}{-z-d}$$

Divide -2z+59 by -z-d.

$$p=-\frac{59-2z}{z+d}$$