Solve 100mum*150mul=50mul*c

$$100 \mu m \times 150 \mu l = 50 \mu l \times c$$

Solve for c

$$\left\{\begin{matrix}\\c=300m\mu \text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&l=0\text{ or }\mu =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \mu and \mu to get \mu ^{2}.

$$100\mu ^{2}m\times 150l=50\mu lc$$

Multiply 100 and 150 to get 15000.

$$15000\mu ^{2}ml=50\mu lc$$

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

$$50\mu lc=15000\mu ^{2}ml$$

The equation is in standard form.

$$50l\mu c=15000lm\mu ^{2}$$

Divide both sides by 50\mu l.

$$\frac{50l\mu c}{50l\mu }=\frac{15000lm\mu ^{2}}{50l\mu }$$

Dividing by 50\mu l undoes the multiplication by 50\mu l.

$$c=\frac{15000lm\mu ^{2}}{50l\mu }$$

Divide 15000\mu ^{2}ml by 50\mu l.

$$c=300m\mu$$

Solve for l

$$\left\{\begin{matrix}\\l=0\text{, }&\text{unconditionally}\\l\in \mathrm{R}\text{, }&c=300m\mu \text{ or }\mu =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \mu and \mu to get \mu ^{2}.

$$100\mu ^{2}m\times 150l=50\mu lc$$

Multiply 100 and 150 to get 15000.

$$15000\mu ^{2}ml=50\mu lc$$

Subtract 50\mu lc from both sides.

$$15000\mu ^{2}ml-50\mu lc=0$$

Combine all terms containing l.

$$\left(15000\mu ^{2}m-50\mu c\right)l=0$$

The equation is in standard form.

$$\left(15000m\mu ^{2}-50c\mu \right)l=0$$

Divide 0 by 15000\mu ^{2}m-50\mu c.

$$l=0$$