Solve d=8left(-3a-24a+d-2right)+12a+48a

$$d = 8 \left( -3a-24a+d-2 \right) +12a+48a$$

Solve for a

$$a=\frac{7d}{156}-\frac{4}{39}$$

Steps for Solving Linear Equation

Combine -3a and -24a to get -27a.

$$d=8\left(-27a+d-2\right)+12a+48a$$

Use the distributive property to multiply 8 by -27a+d-2.

$$d=-216a+8d-16+12a+48a$$

Combine -216a and 12a to get -204a.

$$d=-204a+8d-16+48a$$

Combine -204a and 48a to get -156a.

$$d=-156a+8d-16$$

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

$$-156a+8d-16=d$$

Subtract 8d from both sides.

$$-156a-16=d-8d$$

Combine d and -8d to get -7d.

$$-156a-16=-7d$$

Add 16 to both sides.

$$-156a=-7d+16$$

The equation is in standard form.

$$-156a=16-7d$$

Divide both sides by -156.

$$\frac{-156a}{-156}=\frac{16-7d}{-156}$$

Dividing by -156 undoes the multiplication by -156.

$$a=\frac{16-7d}{-156}$$

Divide -7d+16 by -156.

$$a=\frac{7d}{156}-\frac{4}{39}$$

Solve for d

$$d=\frac{156a+16}{7}$$

Steps for Solving Linear Equation

Combine -3a and -24a to get -27a.

$$d=8\left(-27a+d-2\right)+12a+48a$$

Use the distributive property to multiply 8 by -27a+d-2.

$$d=-216a+8d-16+12a+48a$$

Combine -216a and 12a to get -204a.

$$d=-204a+8d-16+48a$$

Combine -204a and 48a to get -156a.

$$d=-156a+8d-16$$

Subtract 8d from both sides.

$$d-8d=-156a-16$$

Combine d and -8d to get -7d.

$$-7d=-156a-16$$

Divide both sides by -7.

$$\frac{-7d}{-7}=\frac{-156a-16}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$d=\frac{-156a-16}{-7}$$

Divide -156a-16 by -7.

$$d=\frac{156a+16}{7}$$