(-5x+3) (-x+6) =0

To solve the equation \((-5x + 3)(-x + 6) = 0\), we can use the zero product property, which states that if a product of two factors equals zero, at least one of the factors must equal zero. 1. Set each factor equal to zero: \(-5x + 3 = 0\) \(-x + 6 = 0\) 2. Solve each equation: For \(-5x + 3 = 0\): \[ -5x = -3 \quad \text{(subtracting 3 from both sides)} \] \[ x = \frac{3}{5} \quad \text{(dividing both sides by -5)} \] For \(-x + 6 = 0\): \[ -x = -6 \quad \text{(subtracting 6 from both sides)} \] \[ x = 6 \quad \text{(dividing both sides by -1)} \] 3. The solutions to the equation \((-5x + 3)(-x + 6) = 0\) are: \[ x = \frac{3}{5} \quad \text{and} \quad x = 6 \]