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Solve for all values of x : 3x(5x-1)-5(5x-1)=0 Answer: x=

Solve for all values of x x :\newline3x(5x−1)−5(5x−1)=0 3 x(5 x-1)-5(5 x-1)=0 \newlineAnswer: x= x=

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Q. Solve for all values of x x :\newline3x(5x−1)−5(5x−1)=0 3 x(5 x-1)-5(5 x-1)=0 \newlineAnswer: x= x=
  1. Factor out common expression: First, notice that the expression (5x−1)(5x-1) is common to both terms on the left side of the equation. We can factor it out.3x(5x−1)−5(5x−1)=(5x−1)(3x−5)3x(5x-1) - 5(5x-1) = (5x-1)(3x-5)
  2. Apply zero product property: Now that we have factored the equation, we can use the zero product property, which states that 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:\newline5x−1=05x - 1 = 0 or 3x−5=03x - 5 = 0
  3. Solve for x in first equation: Solve the first equation 5x−1=05x - 1 = 0 for x.\newlineAdd 11 to both sides:\newline5x=15x = 1\newlineNow divide by 55:\newlinex=15x = \frac{1}{5}
  4. Solve for x in second equation: Solve the second equation 3x−5=03x - 5 = 0 for x.\newlineAdd 55 to both sides:\newline3x=53x = 5\newlineNow divide by 33:\newlinex=53x = \frac{5}{3}

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