Solve b_{n}=4a_{n}-6n+15

$$b _ { n } = 4 a _ { n } - 6 n + 15$$

Solve for a_n

$$a_{n}=\frac{6n+b_{n}-15}{4}$$

Steps for Solving Linear Equation

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

$$4a_{n}-6n+15=b_{n}$$

Add 6n to both sides.

$$4a_{n}+15=b_{n}+6n$$

Subtract 15 from both sides.

$$4a_{n}=b_{n}+6n-15$$

The equation is in standard form.

$$4a_{n}=6n+b_{n}-15$$

Divide both sides by 4.

$$\frac{4a_{n}}{4}=\frac{6n+b_{n}-15}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a_{n}=\frac{6n+b_{n}-15}{4}$$

Divide b_{n}+6n-15 by 4.

$$a_{n}=\frac{b_{n}}{4}+\frac{3n}{2}-\frac{15}{4}$$

Solve for b_n

$$b_{n}=15+4a_{n}-6n$$