Solve 6[a+5d]=9[a+8d]

$$6 [ a + 5 d ] = 9 [ a + 8 d ]$$

Solve for a

$$a=-14d$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by a+5d.

$$6a+30d=9\left(a+8d\right)$$

Use the distributive property to multiply 9 by a+8d.

$$6a+30d=9a+72d$$

Subtract 9a from both sides.

$$6a+30d-9a=72d$$

Combine 6a and -9a to get -3a.

$$-3a+30d=72d$$

Subtract 30d from both sides.

$$-3a=72d-30d$$

Combine 72d and -30d to get 42d.

$$-3a=42d$$

Divide both sides by -3.

$$\frac{-3a}{-3}=\frac{42d}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$a=\frac{42d}{-3}$$

Divide 42d by -3.

$$a=-14d$$

Solve for d

$$d=-\frac{a}{14}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by a+5d.

$$6a+30d=9\left(a+8d\right)$$

Use the distributive property to multiply 9 by a+8d.

$$6a+30d=9a+72d$$

Subtract 72d from both sides.

$$6a+30d-72d=9a$$

Combine 30d and -72d to get -42d.

$$6a-42d=9a$$

Subtract 6a from both sides.

$$-42d=9a-6a$$

Combine 9a and -6a to get 3a.

$$-42d=3a$$

Divide both sides by -42.

$$\frac{-42d}{-42}=\frac{3a}{-42}$$

Dividing by -42 undoes the multiplication by -42.

$$d=\frac{3a}{-42}$$

Divide 3a by -42.

$$d=-\frac{a}{14}$$