You can take your plants with you when you move without harming them.
Here are some tips:

Call your local U.S. Department of Agriculture to check on regulations if moving from one state to another. Many states have restrictions on certain kinds of plants to prevent importing bugs or pests that can destroy valuable cash crops in that state.

A couple of weeks before you move, prune plants to facilitate packing. Consult a florist or a plant book for instructions.

A week before your move, put your plants in a black plastic bag with a bug/pest strip, conventional flea collar or bug powder in the bag before you put the plant in. Close the bag and place in a cool area overnight. This will kill any pests on the plant or in the soil.

The day before your move, place the plants in cardboard containers. Make sure they are held in place by dampened newspaper or packing paper. Use paper to cushion the leaves and place a final layer of wet paper on top to keep them moist. Water the plants normally in summer, a little less in winter.

On the day of your move, set the boxes aside and mark “DO NOT LOAD” so they won’t be taken on the moving van.

On the day you leave, close boxes, punch air holes in the top and load in your car.

When on the road, be careful where you park your car. Look for a shaded area in the summer and a sunny spot in the winter.

Unpack the plants as soon as you can after arriving. Remove plants through the bottom of the box in order to avoid breaking the stems. Do not expose the plants to too much sunlight at first. Let them get accustomed to more light gradually.

If you must leave your plants behind, then take cuttings. Put them in a plastic bag with wet paper towels around them.