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Solve for xx.\newline41x2+21x=041x^2 + 21x = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinex = ____

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Q. Solve for xx.\newline41x2+21x=041x^2 + 21x = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinex = ____
  1. Factor GCF and Equate: Factor out the greatest common factor (GCF) from the equation 41x2+21x=041x^2 + 21x = 0. The GCF of 41x241x^2 and 21x21x is xx. Factor out xx from each term. x(41x+21)=0x(41x + 21) = 0
  2. Set and Solve for x: Set each factor equal to zero and solve for x.\newlineFirst, set xx equal to zero:\newlinex=0x = 0\newlineThen, set the other factor equal to zero:\newline41x+21=041x + 21 = 0
  3. Solve 41x+21=041x + 21 = 0: Solve the equation 41x+21=041x + 21 = 0 for xx.\newlineSubtract 2121 from both sides of the equation to isolate the term with xx.\newline41x+21−21=0−2141x + 21 - 21 = 0 - 21\newline41x=−2141x = -21\newlineDivide both sides by 4141 to solve for xx.\newlinex=−2141x = -\frac{21}{41}
  4. Write Solutions: Write the values of xx. We have found two solutions where the equation 41x2+21x=041x^2 + 21x = 0 is true: x=0x = 0 and x=−2141x = -\frac{21}{41}.

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