(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:

\[ x = -\frac{2}{5} \quad \text{and} \quad x = -4 \]