Factorize. 4x² -43x-15=0

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Identify Factors for AC Method: We need to factor the quadratic equation 4x² - 43x - 15 = 0. To do this, we will use the AC method, where A is the coefficient of x², B is the coefficient of x, and C is the constant term. We need to find two numbers that multiply to A*C (4*-15 = -60) and add up to B (-43).List Factor Pairs: List the pairs of factors of -60 that could add up to -43. The pairs are (1, -60), (-1, 60), (2, -30), (-2, 30), (3, -20), (-3, 20), (4, -15), (-4, 15), (5, -12), (-5, 12), (6, -10), (-6, 10).Find Correct Pair: Identify the correct pair of factors that add up to -43. The pair is (-48, 5) because -48 + 5 = -43.Rewrite Middle Term: Rewrite the middle term of the quadratic equation using the pair of factors found in the previous step. The equation becomes 4x² - 48x + 5x - 15 = 0.Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms separately. (4x² - 48x) + (5x - 15) = 0.Factor out Common Factor: Factor out the greatest common factor from each group. 4x(x - 12) + 5(x - 3) = 0.Correct Mistake: Notice that the terms in the parentheses are not the same, which means there is a mistake. We need to find a different pair of factors of -60 that add up to -43. The correct pair is (-45, 4) because -45 + 4 = -43. We need to go back and correct the mistake.

Factorize. $4x^2 -43x-15=0$

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Factorize. $4x^2 -43x-15=0$