(х+8)(4х-2)=0

To solve the equation \((x+8)(4x-2)=0\), we can use the Zero Product Property, which states that if the product of two numbers is zero, then at least one of the numbers must be zero.

So, we set each factor to zero:

1. \(x + 8 = 0\)
2. \(4x - 2 = 0\)

Now, let's solve each equation:

1. For \(x + 8 = 0\): \[ x = -8 \]

2. For \(4x - 2 = 0\): \[ 4x = 2 \\ x = \frac{2}{4} = \frac{1}{2} \]

Thus, the solutions to the equation \((x+8)(4x-2)=0\) are: \[ x = -8 \quad \text{and} \quad x = \frac{1}{2} \]