Solve for a 9a² = 16a college intermediate algebra

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

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