Woo (verb)

1. To seek the love, affection, or hand of (someone) with the intent to marry or establish a romantic relationship.
2. To seek the favor, support, or custom of (someone).
3. To seek to gain (something).

Origin:

Late middle english: from old english wōgian "to pursue, strive after", of germanic origin.

Examples:

1. He woos her with flowers and chocolates.
2. The company is trying to woo new customers.
3. She woos him with her beauty.
4. The politician is trying to woo the vote of the electorate.
5. They are trying to woo the company to invest in their city.