ORLANDO (CNN) -- Former Secretary of State Hillary Clinton didn't wait long to applaud the veto of an Arizona law that would have allowed businesses that asserted their religious beliefs the right to deny service to gay and lesbian customers.

In the first minutes of a speech at the University of Miami Wednesday night, Clinton lauded the fact that Arizona Gov. Jan Brewer -- a Republican -- vetoed the legislation that supporters said protected religious liberty.

"Thankfully the governor of Arizona has vetoed the discriminatory legislation that was passed, recognizing that inclusive leadership is really what the 21st century is all about," Clinton said to the 6,000 people who assembled at the south Florida institution.

Brewer announced just hours before Clinton took the stage that she had decided to veto the bill that had created a national firestorm. Brewer said she made the decision she knew was right for her state.

Clinton used the Arizona law to frame the rest of her remarks, weaving between the rights of gays and lesbians to the rights of people with disabilities. The former first lady pulled greatly from her career and her education at Wellesley College and Yale University.

"It is the work of this century to complete the unfinished business of making sure that every girl and boy and every woman and man lives in societies that respect their rights no matter who they are, respects their potential and their talents, gives them the opportunities that every human being deserves, no matter where you were born, no matter the color of your skin, no matter your religion, your ethnicity, or whom you love," Clinton said to applause.

As much as Clinton's speech looked back at her history, though, there were also overarching forward-looking themes in her remarks.

"I hope that your generation will be a true participation generation," she said. "I hope you will find ways to make sure that the barriers that too often divide us are torn down once and for all."

Clinton also commended the young people in the audience for being the "most open-minded and tolerant we have ever seen."

Clinton's speech comes as the former secretary of state eyes a presidential run in 2016. She is the frontrunner for her party's nomination, with poll after poll showing she laps all other possible Democratic challengers.

Despite being asked at every event she attends, Clinton has yet to say whether she will run or not.

If she runs, however, Clinton will have to capture the support of young voters, a constituency that President Barack Obama used to catapult past Clinton in the 2008 race for the Democratic nomination.

Clinton's remarks at University of Miami appear to be an effort to do that.

According to university, roughly 3,200 students watched Clinton speak and many lined up for hours to get into the event.

Students responded generally positively to Clinton's remarks. While one student said Clinton didn't answer all the questions, many said they found her "spontaneous," "motherly," "unscripted" and "funny."

"She has a quality no male candidate has," said one female student, "She's more human."

The former first lady has a number of upcoming events at college and universities.

Next week, Clinton will speak at the University of California-Los Angeles and in April, she will speak at Simmons College and the University of Connecticut.

As is the case with nearly every Clinton event, her decision about whether she will run for president or not in 2016 came up.

A student submitted a question asking in Clinton could define what the "TBD" in her Twitter bio meant.

To round of laughs, Clinton answered: "Well I would really like to, but I have no characters left. I will certainly ponder that."

-- CNN's Rachel Streitfeld and Brianna Keilar contributed to this report.