Solve 2(10-5K)=[n(K-2)+(6-3K)]

$$2 ( 10 - 5 K ) = [ n ( K - 2 ) + ( 6 - 3 K ) ]$$

Solve for K (complex solution)

$$\left\{\begin{matrix}\\K=2\text{, }&\text{unconditionally}\\K\in \mathrm{C}\text{, }&n=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 10-5K.

$$20-10K=n\left(K-2\right)+6-3K$$

Use the distributive property to multiply n by K-2.

$$20-10K=nK-2n+6-3K$$

Subtract nK from both sides.

$$20-10K-nK=-2n+6-3K$$

Add 3K to both sides.

$$20-10K-nK+3K=-2n+6$$

Combine -10K and 3K to get -7K.

$$20-7K-nK=-2n+6$$

Subtract 20 from both sides.

$$-7K-nK=-2n+6-20$$

Subtract 20 from 6 to get -14.

$$-7K-nK=-2n-14$$

Combine all terms containing K.

$$\left(-7-n\right)K=-2n-14$$

The equation is in standard form.

$$\left(-n-7\right)K=-2n-14$$

Divide both sides by -7-n.

$$\frac{\left(-n-7\right)K}{-n-7}=\frac{-2n-14}{-n-7}$$

Dividing by -7-n undoes the multiplication by -7-n.

$$K=\frac{-2n-14}{-n-7}$$

Divide -2n-14 by -7-n.

$$K=2$$

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=-7\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&K=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 10-5K.

$$20-10K=n\left(K-2\right)+6-3K$$

Use the distributive property to multiply n by K-2.

$$20-10K=nK-2n+6-3K$$

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

$$nK-2n+6-3K=20-10K$$

Subtract 6 from both sides.

$$nK-2n-3K=20-10K-6$$

Subtract 6 from 20 to get 14.

$$nK-2n-3K=14-10K$$

Add 3K to both sides.

$$nK-2n=14-10K+3K$$

Combine -10K and 3K to get -7K.

$$nK-2n=14-7K$$

Combine all terms containing n.

$$\left(K-2\right)n=14-7K$$

Divide both sides by -2+K.

$$\frac{\left(K-2\right)n}{K-2}=\frac{14-7K}{K-2}$$

Dividing by -2+K undoes the multiplication by -2+K.

$$n=\frac{14-7K}{K-2}$$

Divide 14-7K by -2+K.

$$n=-7$$

Solve for K

$$\left\{\begin{matrix}\\K=2\text{, }&\text{unconditionally}\\K\in \mathrm{R}\text{, }&n=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 10-5K.

$$20-10K=n\left(K-2\right)+6-3K$$

Use the distributive property to multiply n by K-2.

$$20-10K=nK-2n+6-3K$$

Subtract nK from both sides.

$$20-10K-nK=-2n+6-3K$$

Add 3K to both sides.

$$20-10K-nK+3K=-2n+6$$

Combine -10K and 3K to get -7K.

$$20-7K-nK=-2n+6$$

Subtract 20 from both sides.

$$-7K-nK=-2n+6-20$$

Subtract 20 from 6 to get -14.

$$-7K-nK=-2n-14$$

Combine all terms containing K.

$$\left(-7-n\right)K=-2n-14$$

The equation is in standard form.

$$\left(-n-7\right)K=-2n-14$$

Divide both sides by -7-n.

$$\frac{\left(-n-7\right)K}{-n-7}=\frac{-2n-14}{-n-7}$$

Dividing by -7-n undoes the multiplication by -7-n.

$$K=\frac{-2n-14}{-n-7}$$

Divide -2n-14 by -7-n.

$$K=2$$

Solve for n

$$\left\{\begin{matrix}\\n=-7\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&K=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 10-5K.

$$20-10K=n\left(K-2\right)+6-3K$$

Use the distributive property to multiply n by K-2.

$$20-10K=nK-2n+6-3K$$

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

$$nK-2n+6-3K=20-10K$$

Subtract 6 from both sides.

$$nK-2n-3K=20-10K-6$$

Subtract 6 from 20 to get 14.

$$nK-2n-3K=14-10K$$

Add 3K to both sides.

$$nK-2n=14-10K+3K$$

Combine -10K and 3K to get -7K.

$$nK-2n=14-7K$$

Combine all terms containing n.

$$\left(K-2\right)n=14-7K$$

Divide both sides by -2+K.

$$\frac{\left(K-2\right)n}{K-2}=\frac{14-7K}{K-2}$$

Dividing by -2+K undoes the multiplication by -2+K.

$$n=\frac{14-7K}{K-2}$$

Divide 14-7K by -2+K.

$$n=-7$$