Solve S=3n-2n^2B

$$S = 3 n - 2 n ^ { 2 } B$$

Solve for B

$$\left\{\begin{matrix}B=\frac{3n-S}{2n^{2}}\text{, }&n\neq 0\\B\in \mathrm{R}\text{, }&S=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$3n-2n^{2}B=S$$

Subtract 3n from both sides.

$$-2n^{2}B=S-3n$$

The equation is in standard form.

$$\left(-2n^{2}\right)B=S-3n$$

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

$$\frac{\left(-2n^{2}\right)B}{-2n^{2}}=\frac{S-3n}{-2n^{2}}$$

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

$$B=\frac{S-3n}{-2n^{2}}$$

Divide S-3n by -2n^{2}.

$$B=-\frac{S-3n}{2n^{2}}$$

Solve for S

$$S=n\left(3-2Bn\right)$$