Only one side of the accounting equation will be affected when one asset is used to acquire another asset or to replace another asset, when one liability replaces another liability, when stock is issued to replace a liability, when a cash dividend or stock dividend is declared. There are many other situations as well.
Here are some specific examples when only the left side of the accounting equation is affected. 1) A customer cannot pay an amount it owes and provides the company with a notes receivable. The company's asset Accounts Receivable will decrease and its asset Notes Receivable will increase. 2) A company prepays its insurance. As a result its asset Cash decreases and its asset Prepaid Insurance increases. 3) A company buys equipment for cash. The asset Cash decreases and the asset Equipment increases.
Here are some transactions that will affect only the right side of the accounting equation. 1) A company refinances its short-term debt with long-term debt. Short-term liabilities will decrease and long-term liabilities will increase. 2) A corporation issues common stock to replace its convertible bonds. The result is that liabilities decrease and stockholders' equity increases. 3) A corporation declares a cash dividend. A current liability Dividends Payable is created and the Retained Earnings (part of stockholders' equity) will decrease. 4) A stock dividend is declared. The paid-in capital section of stockholders' equity will increase and the retained earnings section will decrease.