Solve 0=n/2[60+(n-1)x-1]

$$0 = \frac { n } { 2 } [ 60 + ( n - 1 ) x - 1 ]$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{59}{n-1}\text{, }&n\neq 1\\x\in \mathrm{C}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$0=n\left(60+\left(n-1\right)x-1\right)$$

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

$$0=n\left(60+nx-x-1\right)$$

Subtract 1 from 60 to get 59.

$$0=n\left(59+nx-x\right)$$

Use the distributive property to multiply n by 59+nx-x.

$$0=59n+xn^{2}-nx$$

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

$$59n+xn^{2}-nx=0$$

Subtract 59n from both sides. Anything subtracted from zero gives its negation.

$$xn^{2}-nx=-59n$$

Combine all terms containing x.

$$\left(n^{2}-n\right)x=-59n$$

Divide both sides by n^{2}-n.

$$\frac{\left(n^{2}-n\right)x}{n^{2}-n}=-\frac{59n}{n^{2}-n}$$

Dividing by n^{2}-n undoes the multiplication by n^{2}-n.

$$x=-\frac{59n}{n^{2}-n}$$

Divide -59n by n^{2}-n.

$$x=-\frac{59}{n-1}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{59}{n-1}\text{, }&n\neq 1\\x\in \mathrm{R}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$0=n\left(60+\left(n-1\right)x-1\right)$$

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

$$0=n\left(60+nx-x-1\right)$$

Subtract 1 from 60 to get 59.

$$0=n\left(59+nx-x\right)$$

Use the distributive property to multiply n by 59+nx-x.

$$0=59n+xn^{2}-nx$$

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

$$59n+xn^{2}-nx=0$$

Subtract 59n from both sides. Anything subtracted from zero gives its negation.

$$xn^{2}-nx=-59n$$

Combine all terms containing x.

$$\left(n^{2}-n\right)x=-59n$$

Divide both sides by n^{2}-n.

$$\frac{\left(n^{2}-n\right)x}{n^{2}-n}=-\frac{59n}{n^{2}-n}$$

Dividing by n^{2}-n undoes the multiplication by n^{2}-n.

$$x=-\frac{59n}{n^{2}-n}$$

Divide -59n by n^{2}-n.

$$x=-\frac{59}{n-1}$$

Solve for n

$$\left\{\begin{matrix}\\n=0\text{, }&\text{unconditionally}\\n=\frac{x-59}{x}\text{, }&x\neq 0\end{matrix}\right.$$