Solve J=50dm^{3}+10^{7}mm^{3}+3.10^4cm^3+10^16mum^3

$$J = 50 dm ^ { 3 } + 10 ^ { 7 } mm ^ { 3 } + 3.10 ^ { 4 } cm ^ { 3 } + 10 ^ { 16 } \mu m ^ { 3 }$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{500000d}{923521}-\frac{100000000000m}{923521}-\frac{100000000000000000000\mu }{923521}+\frac{10000J}{923521m^{3}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&J=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$J=50dm^{3}+10^{7}m^{4}+3.1^{4}cm^{3}+10^{16}\mu m^{3}$$

Calculate 10 to the power of 7 and get 10000000.

$$J=50dm^{3}[phone]m^{4}+3.1^{4}cm^{3}+10^{16}\mu m^{3}$$

Calculate 3.1 to the power of 4 and get 92.3521.

$$J=50dm^{3}[phone]m^{4}+92.3521cm^{3}+10^{16}\mu m^{3}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$J=50dm^{3}[phone]m^{4}+92.3521cm^{3}+10000000000000000\mu m^{3}$$

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

$$50dm^{3}[phone]m^{4}+92.3521cm^{3}+10000000000000000\mu m^{3}=J$$

Subtract 50dm^{3} from both sides.

$$10000000m^{4}+92.3521cm^{3}+10000000000000000\mu m^{3}=J-50dm^{3}$$

Subtract 10000000m^{4} from both sides.

$$92.3521cm^{3}+10000000000000000\mu m^{3}=J-50dm^{3}-10000000m^{4}$$

Subtract 10000000000000000\mu m^{3} from both sides.

$$92.3521cm^{3}=J-50dm^{3}-10000000m^{4}-10000000000000000\mu m^{3}$$

The equation is in standard form.

$$\frac{923521m^{3}}{10000}c=J-10000000000000000\mu m^{3}-50dm^{3}-10000000m^{4}$$

Divide both sides by 92.3521m^{3}.

$$\frac{10000\times \frac{923521m^{3}}{10000}c}{923521m^{3}}=\frac{10000\left(J-10000000000000000\mu m^{3}-50dm^{3}-10000000m^{4}\right)}{923521m^{3}}$$

Dividing by 92.3521m^{3} undoes the multiplication by 92.3521m^{3}.

$$c=\frac{10000\left(J-10000000000000000\mu m^{3}-50dm^{3}-10000000m^{4}\right)}{923521m^{3}}$$

Divide J-50dm^{3}-10000000m^{4}-10000000000000000\mu m^{3} by 92.3521m^{3}.

$$c=-\frac{500000d}{923521}-\frac{100000000000m}{923521}-\frac{100000000000000000000\mu }{923521}+\frac{10000J}{923521m^{3}}$$

Solve for J

$$J=\frac{\left(100000000000m+500000d+923521c+100000000000000000000\mu \right)m^{3}}{10000}$$