To solve the equation \((x - 7)(7x - 5) = 0\), we set each factor equal to zero:
- \(x - 7 = 0\)
- \(7x - 5 = 0\)
Now we solve each equation:
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For \(x - 7 = 0\): \[ x = 7 \]
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For \(7x - 5 = 0\): \[ 7x = 5 \] \[ x = \frac{5}{7} \]
Therefore, the solutions to the equation \((x - 7)(7x - 5) = 0\) are: \[ x = 7 \quad \text{and} \quad x = \frac{5}{7} \]