Solve the equation for all values of x

(x−7)(7x−5)=0

1 answer

To solve the equation \((x - 7)(7x - 5) = 0\), we set each factor equal to zero:

  1. \(x - 7 = 0\)
  2. \(7x - 5 = 0\)

Now we solve each equation:

  1. For \(x - 7 = 0\): \[ x = 7 \]

  2. For \(7x - 5 = 0\): \[ 7x = 5 \] \[ x = \frac{5}{7} \]

Therefore, the solutions to the equation \((x - 7)(7x - 5) = 0\) are: \[ x = 7 \quad \text{and} \quad x = \frac{5}{7} \]