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.

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

Multiply 325 and 2 to get 650.

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

Use the distributive property to multiply n by 8b+\left(n-1\right)\times \left(-3\right).

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

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

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

Subtract n\left(\left(n-1\right)\times \left(-3\right)\right) from both sides.

$$8nb=650-n\left(\left(n-1\right)\times \left(-3\right)\right)$$

Reorder the terms.

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

The equation is in standard form.

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

Divide both sides by 8n.

$$\frac{8nb}{8n}=\frac{3n\left(n-1\right)+650}{8n}$$

Dividing by 8n undoes the multiplication by 8n.

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

Divide 3\left(n-1\right)n+650 by 8n.

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

Solve for n

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

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