Solve 3n=k(1-n)

$$3 n = k ( 1 - n )$$

Solve for k

$$k=-\frac{3n}{n-1}$$

$$n\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 1-n.

$$3n=k-kn$$

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

$$k-kn=3n$$

Combine all terms containing k.

$$\left(1-n\right)k=3n$$

Divide both sides by 1-n.

$$\frac{\left(1-n\right)k}{1-n}=\frac{3n}{1-n}$$

Dividing by 1-n undoes the multiplication by 1-n.

$$k=\frac{3n}{1-n}$$

Solve for n

$$n=\frac{k}{k+3}$$

$$k\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 1-n.

$$3n=k-kn$$

Add kn to both sides.

$$3n+kn=k$$

Combine all terms containing n.

$$\left(3+k\right)n=k$$

The equation is in standard form.

$$\left(k+3\right)n=k$$

Divide both sides by 3+k.

$$\frac{\left(k+3\right)n}{k+3}=\frac{k}{k+3}$$

Dividing by 3+k undoes the multiplication by 3+k.

$$n=\frac{k}{k+3}$$