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Solve for tt.\newline6t2−11t=06t^2 - 11t = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinet=t = ____

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Q. Solve for tt.\newline6t2−11t=06t^2 - 11t = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinet=t = ____
  1. Factor GCF and Factorize: Factor out the greatest common factor (GCF) of the terms in the equation 6t2−11t=06t^2 - 11t = 0. The GCF of 6t26t^2 and −11t-11t is tt. Factor out tt from each term. t(6t−11)=0t(6t - 11) = 0
  2. Apply Zero-Product Property: Apply the zero-product property.\newlineIf the product of two factors is zero, then at least one of the factors must be zero.\newlineSet each factor equal to zero and solve for tt.\newlinet=0t = 0\newline6t−11=06t - 11 = 0
  3. Solve for t: Solve the equation 6t−11=06t - 11 = 0 for tt.\newlineAdd 1111 to both sides of the equation.\newline6t=116t = 11\newlineDivide both sides by 66 to isolate tt.\newlinet=116t = \frac{11}{6}
  4. Write Solutions: Write the values of tt. We have found two solutions where the equation 6t2−11t=06t^2 - 11t = 0 is true. t=0t = 0, 116\frac{11}{6}

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