T AMPA — Mitt Romney will have many audiences, with their often conflicting agendas, to persuade when he accepts his party’s nomination at the Republican National Convention on Thursday night.

It will be his chance to show Americans that his evolving positions over the years — on healthcare reform, environmental protection and women’s reproductive rights — come from hard lessons learned and strong insights reached from years of experience as a governor and businessman not from political expediency. It will be a tough balancing act:

• Independent voters are searching for fiscal discipline in Washington balanced with a social safety net.

• Moderate women voters are concerned about the GOP’s recent hard right turn on reproductive rights, including contraception.

• Hispanic- and Caribbean-American voters, as popular former Florida Gov. Jeb Bush and Sen. Marco Rubio stress, want to be treated with respect not as outcasts over the immigration issue.

• Elderly voters expect Social Security and Medicare secured and not raided to pay for other programs or balance the books.

• African Americans, for their part, see no future in the party of Lincoln, but, they, like all Americans regardless of party affiliation, yearn for a strong economic turnaround to restore the dwindling middle class after President Obama inherited the worst downturn since the Great Depression.

This will be Mr. Romney’s opportunity to speak directly to an estimated 40 million Americans who will watch the televised coronation of the GOP’s choice for president. He will be unfettered by media spin, to make his case directly that a President Romney would do better for this country than President Obama has been able to do.

Ann Romney, as any loving wife would, softened her husband’s image in her Tuesday convention speech and asked the nation to trust him. In a way it was an odd plea, as Mr. Romney is no Johnny Come Lately to politics and has a record to follow. As Massachusetts governor he moved on several reforms, from education to healthcare. Indeed, “Obamacare” was fashioned after Mr. Romney’s Massachusetts plan, which he now says should be each state’s decision and not a national program.

The economy remains the issue Americans most worry about, but in that arena Mr. Romney’s record at Bain Capital as a jobs creator has been overshadowed by partisan critics’ reminders about the companies that were shut down and the jobs that were sent overseas.

Mr. Romney has one more challenge that will prove his mettle: He will have to gain the trust of critics within his own party. Can he lead the Ron Paul libertarians who think Mr. Romney is not fiscally conservative enough and, at the other extreme, the social conservatives and evangelicals not sure what to make about Mr. Romney’s Mormon roots? Or will he, as the campaign has shown so far, let those extremist voices lead him?

In his convention address, New Jersey Gov. Chris Christie, in his typical blunt populist style, laid out the sacrifice and “hard truths” that are needed to restore fiscal order to a federal budget run amok: “Real leaders don’t follow polls. Real leaders change polls.”

In this neck-in-neck race that will be decided by Florida, a must-win “purple” swing state, Mr. Romney will have to show he can lead with an open mind and heart.