Use factoring and the zero-product property to solve the following problems.

Answer:see explanationStep-by-step explanation:Divide through by 22a² - 5a + 3 = 0 To factor the quadraticConsider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the x- termproduct = 2 × 3 = 6 and sum = - 5The factors are - 2 and - 3Use the factors to split the a- term2a² - 2a - 3a + 3 = 0 ( factor the first/second and third/fourth terms )2a(a - 1) - 3(a - 1) = 0 ← factor out (a - 1)(a - 1)(2a - 3) = 0Equate each factor to zero and solve for aa - 1 = 0 ⇒ a = 12a - 3 = 0 ⇒ 2a = 3 ⇒ a = [tex]\frac{3}{2}[/tex]