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Solve for zz.\newline29z2−20z=029z^2 - 20z = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinez=z = ____

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Q. Solve for zz.\newline29z2−20z=029z^2 - 20z = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinez=z = ____
  1. Factor GCF: Factor out the greatest common factor (GCF) from the equation 29z2−20z=029z^2 - 20z = 0. The GCF of 29z229z^2 and 20z20z is zz. Factor out zz from each term. z(29z−20)=0z(29z - 20) = 0
  2. Set Equal Zero: Set each factor equal to zero and solve for zz.\newlineFirst, set zz equal to zero:\newlinez=0z = 0\newlineThis is one solution.
  3. Solve for z: Now set the other factor equal to zero and solve for z:\newline29z−20=029z - 20 = 0\newlineAdd 2020 to both sides to isolate the term with z.\newline29z=2029z = 20\newlineDivide both sides by 2929 to solve for z.\newlinez=2029z = \frac{20}{29}\newlineThis is the second solution.
  4. Write Solutions: Write the values of zz. We have two solutions from the factored equation z(29z−20)=0z(29z - 20) = 0. The equation will be true if either z=0z = 0 or 29z−20=029z - 20 = 0. z=0z = 0, 2029\frac{20}{29}

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