Solve the equation for all values of x

Question

(x−7)(7x−5)=0

Answer 1

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: \[ x = 7 \quad \text{and} \quad x = \frac{5}{7} \]