(5х+2)(-х-4)=0

To solve the equation \((5x + 2)(-x - 4) = 0\), we will use the zero product property, which states that if a product of two factors equals zero, then at least one of the factors must be zero. This gives us two equations to solve: 1. \(5x + 2 = 0\) 2. \(-x - 4 = 0\) **Solving the first equation:** \[ 5x + 2 = 0 \] Subtract 2 from both sides: \[ 5x = -2 \] Now divide by 5: \[ x = -\frac{2}{5} \] **Solving the second equation:** \[ -x - 4 = 0 \] Add \(x\) to both sides: \[ -x = 4 \] Now multiply by -1: \[ x = -4 \] Thus, the solutions to the equation \((5x + 2)(-x - 4) = 0\) are: \[ x = -\frac{2}{5} \quad \text{and} \quad x = -4 \]