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Solve for dd.\newline26d2+31d=026d^2 + 31d = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlined=d = ____

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Q. Solve for dd.\newline26d2+31d=026d^2 + 31d = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlined=d = ____
  1. Factor GCF: Factor out the greatest common factor (GCF).\newlineThe GCF of 26d226d^2 and 31d31d is dd.\newlineFactor out the GCF from each term in 26d2+31d=026d^2 + 31d = 0.\newlined(26d+31)=0d(26d + 31) = 0
  2. Apply Zero Product Property: Apply the zero product property.\newlineIf a product of factors equals zero, then at least one of the factors must be zero.\newlineSo, set each factor equal to zero and solve for dd.\newlined=0d = 0\newline26d+31=026d + 31 = 0
  3. Solve Equation for dd: Solve the equation 26d+31=026d + 31 = 0 for dd.\newlineSubtract 3131 from both sides of the equation.\newline26d=−3126d = -31\newlineDivide both sides by 2626 to isolate dd.\newlined=−3126d = -\frac{31}{26}\newlineSimplify the fraction.\newlined=−3126d = -\frac{31}{26} (This fraction is already in simplest form.)
  4. Write Values of dd: Write the values of dd. We found: d(26d+31)=0d(26d + 31) = 0. This equation will be true if either d=0d = 0 or 26d+31=026d + 31 = 0. d=0,−3126d = 0, -\frac{31}{26}

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