Solve 10m(n-p)=q

$$10 m ( n - p ) = q$$

Solve for m

$$\left\{\begin{matrix}m=\frac{q}{10\left(n-p\right)}\text{, }&n\neq p\\m\in \mathrm{R}\text{, }&q=0\text{ and }n=p\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10m by n-p.

$$10mn-10mp=q$$

Combine all terms containing m.

$$\left(10n-10p\right)m=q$$

Divide both sides by 10n-10p.

$$\frac{\left(10n-10p\right)m}{10n-10p}=\frac{q}{10n-10p}$$

Dividing by 10n-10p undoes the multiplication by 10n-10p.

$$m=\frac{q}{10n-10p}$$

Divide q by 10n-10p.

$$m=\frac{q}{10\left(n-p\right)}$$

Solve for n

$$\left\{\begin{matrix}n=p+\frac{q}{10m}\text{, }&m\neq 0\\n\in \mathrm{R}\text{, }&q=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10m by n-p.

$$10mn-10mp=q$$

Add 10mp to both sides.

$$10mn=q+10mp$$

The equation is in standard form.

$$10mn=10mp+q$$

Divide both sides by 10m.

$$\frac{10mn}{10m}=\frac{10mp+q}{10m}$$

Dividing by 10m undoes the multiplication by 10m.

$$n=\frac{10mp+q}{10m}$$

Divide q+10mp by 10m.

$$n=p+\frac{q}{10m}$$