Solve mu=12N/(30kg)(10m/s^2)

$$\mu = 12 N / ( 30 kg ) ( 10 m / s ^ { 2 } )$$

Solve for N (complex solution)

$$\left\{\begin{matrix}N=\frac{gk\mu s^{2}}{4m}\text{, }&g\neq 0\text{ and }k\neq 0\text{ and }m\neq 0\text{ and }s\neq 0\\N\in \mathrm{C}\text{, }&\mu =0\text{ and }m=0\text{ and }s\neq 0\text{ and }g\neq 0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30gks^{2}, the least common multiple of 30kg,s^{2}.

$$\mu \times 30gks^{2}=s^{2}\times 12N\times \frac{10m}{s^{2}}$$

Express s^{2}\times \frac{10m}{s^{2}} as a single fraction.

$$\mu \times 30gks^{2}=\frac{s^{2}\times 10m}{s^{2}}\times 12N$$

Cancel out s^{2} in both numerator and denominator.

$$\mu \times 30gks^{2}=10m\times 12N$$

Multiply 10 and 12 to get 120.

$$\mu \times 30gks^{2}=120mN$$

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

$$120mN=\mu \times 30gks^{2}$$

The equation is in standard form.

$$120mN=30gk\mu s^{2}$$

Divide both sides by 120m.

$$\frac{120mN}{120m}=\frac{30gk\mu s^{2}}{120m}$$

Dividing by 120m undoes the multiplication by 120m.

$$N=\frac{30gk\mu s^{2}}{120m}$$

Divide 30\mu gks^{2} by 120m.

$$N=\frac{gk\mu s^{2}}{4m}$$

Solve for N

$$\left\{\begin{matrix}N=\frac{gk\mu s^{2}}{4m}\text{, }&g\neq 0\text{ and }k\neq 0\text{ and }m\neq 0\text{ and }s\neq 0\\N\in \mathrm{R}\text{, }&\mu =0\text{ and }m=0\text{ and }s\neq 0\text{ and }g\neq 0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30gks^{2}, the least common multiple of 30kg,s^{2}.

$$\mu \times 30gks^{2}=s^{2}\times 12N\times \frac{10m}{s^{2}}$$

Express s^{2}\times \frac{10m}{s^{2}} as a single fraction.

$$\mu \times 30gks^{2}=\frac{s^{2}\times 10m}{s^{2}}\times 12N$$

Cancel out s^{2} in both numerator and denominator.

$$\mu \times 30gks^{2}=10m\times 12N$$

Multiply 10 and 12 to get 120.

$$\mu \times 30gks^{2}=120mN$$

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

$$120mN=\mu \times 30gks^{2}$$

The equation is in standard form.

$$120mN=30gk\mu s^{2}$$

Divide both sides by 120m.

$$\frac{120mN}{120m}=\frac{30gk\mu s^{2}}{120m}$$

Dividing by 120m undoes the multiplication by 120m.

$$N=\frac{30gk\mu s^{2}}{120m}$$

Divide 30\mu gks^{2} by 120m.

$$N=\frac{gk\mu s^{2}}{4m}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{4Nm}{k\mu s^{2}}\text{, }&m\neq 0\text{ and }N\neq 0\text{ and }s\neq 0\text{ and }\mu \neq 0\text{ and }k\neq 0\\g\neq 0\text{, }&\left(m=0\text{ or }N=0\right)\text{ and }\mu =0\text{ and }s\neq 0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30gks^{2}, the least common multiple of 30kg,s^{2}.

$$\mu \times 30gks^{2}=s^{2}\times 12N\times \frac{10m}{s^{2}}$$

Express s^{2}\times \frac{10m}{s^{2}} as a single fraction.

$$\mu \times 30gks^{2}=\frac{s^{2}\times 10m}{s^{2}}\times 12N$$

Cancel out s^{2} in both numerator and denominator.

$$\mu \times 30gks^{2}=10m\times 12N$$

Multiply 10 and 12 to get 120.

$$\mu \times 30gks^{2}=120mN$$

The equation is in standard form.

$$30k\mu s^{2}g=120Nm$$

Divide both sides by 30\mu ks^{2}.

$$\frac{30k\mu s^{2}g}{30k\mu s^{2}}=\frac{120Nm}{30k\mu s^{2}}$$

Dividing by 30\mu ks^{2} undoes the multiplication by 30\mu ks^{2}.

$$g=\frac{120Nm}{30k\mu s^{2}}$$

Divide 120mN by 30\mu ks^{2}.

$$g=\frac{4Nm}{k\mu s^{2}}$$

Variable g cannot be equal to 0.

$$g=\frac{4Nm}{k\mu s^{2}}\text{, }g\neq 0$$