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Solve for tt.\newline35t2+19t=035t^2 + 19t = 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.\newline35t2+19t=035t^2 + 19t = 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 and Solve Equation: First, we need to factor the equation to find the values of tt that satisfy the equation 35t2+19t=035t^2 + 19t = 0. The greatest common factor (GCF) of each term is “t”\text{“}t\text{”}. Factor out the GCF from each term in the equation. t(35t+19)=0t(35t + 19) = 0
  2. Apply Zero Product Property: Now we have the factored form of the equation, which is a product of two factors equal to zero. According to the zero product property, if a product of two factors is zero, then at least one of the factors must be zero.\newlineSo, we set each factor equal to zero and solve for tt.\newlineFirst, set t=0t = 0.\newlinet=0t = 0
  3. Solve for t=0t = 0: Next, set the other factor equal to zero and solve for tt.35t+19=035t + 19 = 0Subtract 1919 from both sides to isolate the term with tt.35t=−1935t = -19Now, divide both sides by 3535 to solve for tt.t=−1935t = -\frac{19}{35}
  4. Solve for t=−1935t = -\frac{19}{35}: We have found two values of tt that satisfy the equation.\newlineThe solutions are t=0t = 0 and t=−1935t = -\frac{19}{35}.

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