Solve z^2-2z-48=(z-8)(z+E)

$$z ^ { 2 } - 2 z - 48 = ( z - 8 ) ( z + E )$$

Solve for E (complex solution)

$$\left\{\begin{matrix}\\E=6\text{, }&\text{unconditionally}\\E\in \mathrm{C}\text{, }&z=8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z-8 by z+E.

$$z^{2}-2z-48=z^{2}+zE-8z-8E$$

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

$$z^{2}+zE-8z-8E=z^{2}-2z-48$$

Subtract z^{2} from both sides.

$$zE-8z-8E=z^{2}-2z-48-z^{2}$$

Combine z^{2} and -z^{2} to get 0.

$$zE-8z-8E=-2z-48$$

Add 8z to both sides.

$$zE-8E=-2z-48+8z$$

Combine -2z and 8z to get 6z.

$$zE-8E=6z-48$$

Combine all terms containing E.

$$\left(z-8\right)E=6z-48$$

Divide both sides by -8+z.

$$\frac{\left(z-8\right)E}{z-8}=\frac{6z-48}{z-8}$$

Dividing by -8+z undoes the multiplication by -8+z.

$$E=\frac{6z-48}{z-8}$$

Divide -48+6z by -8+z.

$$E=6$$

Solve for z (complex solution)

$$\left\{\begin{matrix}\\z=8\text{, }&\text{unconditionally}\\z\in \mathrm{C}\text{, }&E=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z-8 by z+E.

$$z^{2}-2z-48=z^{2}+zE-8z-8E$$

Subtract z^{2} from both sides.

$$z^{2}-2z-48-z^{2}=zE-8z-8E$$

Combine z^{2} and -z^{2} to get 0.

$$-2z-48=zE-8z-8E$$

Subtract zE from both sides.

$$-2z-48-zE=-8z-8E$$

Add 8z to both sides.

$$-2z-48-zE+8z=-8E$$

Combine -2z and 8z to get 6z.

$$6z-48-zE=-8E$$

Add 48 to both sides.

$$6z-zE=-8E+48$$

Combine all terms containing z.

$$\left(6-E\right)z=-8E+48$$

The equation is in standard form.

$$\left(6-E\right)z=48-8E$$

Divide both sides by 6-E.

$$\frac{\left(6-E\right)z}{6-E}=\frac{48-8E}{6-E}$$

Dividing by 6-E undoes the multiplication by 6-E.

$$z=\frac{48-8E}{6-E}$$

Divide -8E+48 by 6-E.

$$z=8$$

Solve for E

$$\left\{\begin{matrix}\\E=6\text{, }&\text{unconditionally}\\E\in \mathrm{R}\text{, }&z=8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z-8 by z+E.

$$z^{2}-2z-48=z^{2}+zE-8z-8E$$

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

$$z^{2}+zE-8z-8E=z^{2}-2z-48$$

Subtract z^{2} from both sides.

$$zE-8z-8E=z^{2}-2z-48-z^{2}$$

Combine z^{2} and -z^{2} to get 0.

$$zE-8z-8E=-2z-48$$

Add 8z to both sides.

$$zE-8E=-2z-48+8z$$

Combine -2z and 8z to get 6z.

$$zE-8E=6z-48$$

Combine all terms containing E.

$$\left(z-8\right)E=6z-48$$

Divide both sides by -8+z.

$$\frac{\left(z-8\right)E}{z-8}=\frac{6z-48}{z-8}$$

Dividing by -8+z undoes the multiplication by -8+z.

$$E=\frac{6z-48}{z-8}$$

Divide -48+6z by -8+z.

$$E=6$$

Solve for z

$$\left\{\begin{matrix}\\z=8\text{, }&\text{unconditionally}\\z\in \mathrm{R}\text{, }&E=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z-8 by z+E.

$$z^{2}-2z-48=z^{2}+zE-8z-8E$$

Subtract z^{2} from both sides.

$$z^{2}-2z-48-z^{2}=zE-8z-8E$$

Combine z^{2} and -z^{2} to get 0.

$$-2z-48=zE-8z-8E$$

Subtract zE from both sides.

$$-2z-48-zE=-8z-8E$$

Add 8z to both sides.

$$-2z-48-zE+8z=-8E$$

Combine -2z and 8z to get 6z.

$$6z-48-zE=-8E$$

Add 48 to both sides.

$$6z-zE=-8E+48$$

Combine all terms containing z.

$$\left(6-E\right)z=-8E+48$$

The equation is in standard form.

$$\left(6-E\right)z=48-8E$$

Divide both sides by 6-E.

$$\frac{\left(6-E\right)z}{6-E}=\frac{48-8E}{6-E}$$

Dividing by 6-E undoes the multiplication by 6-E.

$$z=\frac{48-8E}{6-E}$$

Divide -8E+48 by 6-E.

$$z=8$$