Use the zero product property to find the solution to the equation 6x^2 -5x =56

Answer:   x = {-8/3, 7/2}Step-by-step explanation:To use the zero product property, you need the equation in the form of a product that is equal to zero. We can get that by subtracting 56 and factoring the resulting equation.   6x^2 -5x -56 = 0   (3x +8)(2x -7) = 0The zero product property tells us this product is zero only when the factors are zero:   3x +8 = 0   ⇒   x = -8/3   2x -7 = 0   ⇒   x = 7/2The solution is x = {-8/3, 7/2}._____Comment on factoringConsider the product ...   (ax +b)(cx +d) = (ac)x^2 +(ad +bc)x +(bd)Now consider the product of first and last term coefficients compared to the coefficient of the middle term:   acbd = (ad)(bc)  vs.  ad+bcWe see that the coefficient of the middle term is the sum of two of the factors of the first·last product. This means we want factors of 6·(-56) that have a sum of -5.   6(-56) = -(2^4)(3)(7) . . . . has 20 divisors. We're looking for factors that are nearly equal. The clue is given by simplifying the above factoring:   = -(16)(21) = (16)(-21) . . . . the sum of these factors is -5, as we need.Again considering the first-last product and the middle coefficient, we see that we can choose ...   ad = -21, bc = 16; ac = 6, so a=3, c=2, and ...   (a, b, c, d) = (3, 8, 2, -7)These values give us the factors we used above.Note this process gets easier with practice and familiarity with multiplication tables.