We want to solve 9a² = 16a for a.
Because the a is on both sides, a good strategy is to get all the a terms on one side and set it equal to zero. Then we apply the Zero Product Property (if the product is zero then so are its pieces and Factoring.
9a² = 16a
9a² - 16a = 0 <-----subtract 16a from both sides
a (9a - 16) = 0 <-----factor the common a on the left side
a = 0 OR 9a - 16 =0 <----apply Zero Product Property
Since a = 0 is already solved we work on the other equation.
9a - 16 = 0
9a = 16 <----------- add 16 to both sides
a = 16/9 <----------- divide both sides by 9
Thus a = 0 or a = 16/9