Solve 100=n[2*23+(n-1)x-3/2

$$100 = \frac { n [ 2 \times 23 + ( n - 1 ) x - 3 } { 2 }$$

Solve for x

$$x=-\frac{43n-200}{n\left(n-1\right)}$$

$$n\neq 1\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$100\times 2=n\left(2\times 23+\left(n-1\right)x-3\right)$$

Multiply 100 and 2 to get 200.

$$200=n\left(2\times 23+\left(n-1\right)x-3\right)$$

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

$$200=n\left(2\times 23+nx-x-3\right)$$

Use the distributive property to multiply n by 2\times 23+nx-x-3.

$$200=n\left(2\times 23\right)+xn^{2}-nx-3n$$

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

$$n\left(2\times 23\right)+xn^{2}-nx-3n=200$$

Subtract n\left(2\times 23\right) from both sides.

$$xn^{2}-nx-3n=200-n\left(2\times 23\right)$$

Add 3n to both sides.

$$xn^{2}-nx=200-n\left(2\times 23\right)+3n$$

Reorder the terms.

$$xn^{2}-nx=-n\left(2\times 23\right)+3n+200$$

Combine all terms containing x.

$$\left(n^{2}-n\right)x=-n\left(2\times 23\right)+3n+200$$

The equation is in standard form.

$$\left(n^{2}-n\right)x=200-43n$$

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

$$\frac{\left(n^{2}-n\right)x}{n^{2}-n}=\frac{200-43n}{n^{2}-n}$$

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

$$x=\frac{200-43n}{n^{2}-n}$$

Divide -43n+200 by n^{2}-n.

$$x=\frac{200-43n}{n\left(n-1\right)}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{\sqrt{x^{2}+714x+1849}+x-43}{2x}\text{; }n=\frac{-\sqrt{x^{2}+714x+1849}+x-43}{2x}\text{, }&x\neq 0\\n=\frac{200}{43}\approx 4.651162791\text{, }&x=0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{x^{2}+714x+1849}+x-43}{2x}\text{; }n=\frac{-\sqrt{x^{2}+714x+1849}+x-43}{2x}\text{, }&x\leq -20\sqrt{314}-357\text{ or }\left(x\neq 0\text{ and }x\geq 20\sqrt{314}-357\right)\\n=\frac{200}{43}\approx 4.651162791\text{, }&x=0\end{matrix}\right.$$