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Solve for kk.\newline27k2−32k=027k^2 - 32k = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinek = ____

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Q. Solve for kk.\newline27k2−32k=027k^2 - 32k = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinek = ____
  1. Factor GCF: Factor out the greatest common factor (GCF) from the equation 27k2−32k=027k^2 - 32k = 0. The GCF of 27k227k^2 and 32k32k is kk. Factor out kk from each term. k(27k−32)=0k(27k - 32) = 0
  2. Set Equal Solve: Set each factor equal to zero and solve for kk.\newlineFirst, set kk equal to zero:\newlinek=0k = 0\newlineThen, set the other factor equal to zero:\newline27k−32=027k - 32 = 0
  3. Solve for k: Solve the equation 27k−32=027k - 32 = 0 for kk.\newlineAdd 3232 to both sides of the equation to isolate the term with kk.\newline27k−32+32=0+3227k - 32 + 32 = 0 + 32\newline27k=3227k = 32\newlineDivide both sides by 2727 to solve for kk.\newlinek=3227k = \frac{32}{27}
  4. Write Solutions: Write the values of kk. We have found two solutions where the equation will be true: k=0k = 0 and k=3227k = \frac{32}{27}. k=0,3227k = 0, \frac{32}{27}

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