Solve z=(m-2i)(2+4i)s

$$z = ( m - 2 i ) ( 2 + 4 i ) s$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\left(\frac{1}{10}-\frac{1}{5}i\right)z}{s}+2i\text{, }&s\neq 0\\m\in \mathrm{C}\text{, }&z=0\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-2i by 2+4i.

$$z=\left(\left(2+4i\right)m+\left(8-4i\right)\right)s$$

Use the distributive property to multiply \left(2+4i\right)m+\left(8-4i\right) by s.

$$z=\left(2+4i\right)ms+\left(8-4i\right)s$$

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

$$\left(2+4i\right)ms+\left(8-4i\right)s=z$$

Subtract \left(8-4i\right)s from both sides.

$$\left(2+4i\right)ms=z-\left(8-4i\right)s$$

Multiply -1 and 8-4i to get -8+4i.

$$\left(2+4i\right)ms=z+\left(-8+4i\right)s$$

The equation is in standard form.

$$\left(2+4i\right)sm=z+\left(-8+4i\right)s$$

Divide both sides by \left(2+4i\right)s.

$$\frac{\left(2+4i\right)sm}{\left(2+4i\right)s}=\frac{z+\left(-8+4i\right)s}{\left(2+4i\right)s}$$

Dividing by \left(2+4i\right)s undoes the multiplication by \left(2+4i\right)s.

$$m=\frac{z+\left(-8+4i\right)s}{\left(2+4i\right)s}$$

Divide z+\left(-8+4i\right)s by \left(2+4i\right)s.

$$m=\frac{\left(\frac{1}{10}-\frac{1}{5}i\right)z}{s}+2i$$

Solve for s

$$\left\{\begin{matrix}s=\frac{\left(\frac{1}{10}-\frac{1}{5}i\right)z}{m-2i}\text{, }&m\neq 2i\\s\in \mathrm{C}\text{, }&z=0\text{ and }m=2i\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-2i by 2+4i.

$$z=\left(\left(2+4i\right)m+\left(8-4i\right)\right)s$$

Use the distributive property to multiply \left(2+4i\right)m+\left(8-4i\right) by s.

$$z=\left(2+4i\right)ms+\left(8-4i\right)s$$

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

$$\left(2+4i\right)ms+\left(8-4i\right)s=z$$

Combine all terms containing s.

$$\left(\left(2+4i\right)m+\left(8-4i\right)\right)s=z$$

Divide both sides by \left(2+4i\right)m+\left(8-4i\right).

$$\frac{\left(\left(2+4i\right)m+\left(8-4i\right)\right)s}{\left(2+4i\right)m+\left(8-4i\right)}=\frac{z}{\left(2+4i\right)m+\left(8-4i\right)}$$

Dividing by \left(2+4i\right)m+\left(8-4i\right) undoes the multiplication by \left(2+4i\right)m+\left(8-4i\right).

$$s=\frac{z}{\left(2+4i\right)m+\left(8-4i\right)}$$

Divide z by \left(2+4i\right)m+\left(8-4i\right).

$$s=\frac{z}{2\left(\left(1+2i\right)m+\left(4-2i\right)\right)}$$