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Solve for yy.\newline5y2−38y=05y^2 - 38y = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newliney=y = ____

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Q. Solve for yy.\newline5y2−38y=05y^2 - 38y = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newliney=y = ____
  1. Factor GCF: Factor out the greatest common factor (GCF).\newlineThe GCF of 5y25y^2 and 38y38y is yy.\newlineFactor out yy from each term in the equation 5y2−38y=05y^2 - 38y = 0.\newliney(5y−38)=0y(5y - 38) = 0
  2. Apply Zero-Product Property: Apply the zero-product property.\newlineFor the product of factors to be zero, at least one of the factors must be zero.\newlineTherefore, we set each factor equal to zero and solve for yy.\newliney=0y = 0\newline5y−38=05y - 38 = 0
  3. Solve for y: Solve for y when 5y−38=05y - 38 = 0. Add 3838 to both sides of the equation to isolate the term with yy. 5y−38+38=0+385y - 38 + 38 = 0 + 38 5y=385y = 38 Divide both sides by 55 to solve for yy. y=38/5y = 38 / 5 y=7.6y = 7.6 Since the question asks for an integer, proper fraction, or improper fraction, we leave the answer as a fraction. y=38/5y = 38/5

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