Solve 325=n[8b+(n-1)*(-3)]/2

$$325 = \frac { n [ 8 b + ( n - 1 ) \times ( - 3 ) ] } { 2 }$$

Solve for b

$$b=\frac{3n}{8}-\frac{3}{8}+\frac{325}{4n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$325\times 2=n\left(8b+\left(n-1\right)\left(-3\right)\right)$$

Multiply 325 and 2 to get 650.

$$650=n\left(8b+\left(n-1\right)\left(-3\right)\right)$$

Use the distributive property to multiply n-1 by -3.

$$650=n\left(8b-3n+3\right)$$

Use the distributive property to multiply n by 8b-3n+3.

$$650=8nb-3n^{2}+3n$$

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

$$8nb-3n^{2}+3n=650$$

Add 3n^{2} to both sides.

$$8nb+3n=650+3n^{2}$$

Subtract 3n from both sides.

$$8nb=650+3n^{2}-3n$$

The equation is in standard form.

$$8nb=3n^{2}-3n+650$$

Divide both sides by 8n.

$$\frac{8nb}{8n}=\frac{3n^{2}-3n+650}{8n}$$

Dividing by 8n undoes the multiplication by 8n.

$$b=\frac{3n^{2}-3n+650}{8n}$$

Divide 650+3n^{2}-3n by 8n.

$$b=\frac{3n}{8}-\frac{3}{8}+\frac{325}{4n}$$

Solve for n (complex solution)

$$n=-\frac{\sqrt{64b^{2}+48b-7791}}{6}+\frac{4b}{3}+\frac{1}{2}$$

$$n=\frac{\sqrt{64b^{2}+48b-7791}}{6}+\frac{4b}{3}+\frac{1}{2}$$

Solve for n

$$n=-\frac{\sqrt{64b^{2}+48b-7791}}{6}+\frac{4b}{3}+\frac{1}{2}$$

$$n=\frac{\sqrt{64b^{2}+48b-7791}}{6}+\frac{4b}{3}+\frac{1}{2}\text{, }b\geq \frac{5\sqrt{78}}{4}-\frac{3}{8}\text{ or }b\leq -\frac{5\sqrt{78}}{4}-\frac{3}{8}$$