To solve the equation \((3.5 - 7x)(0.1x + 2.3) = 0\), we need to find the values of \(x\) that make the product of the two factors equal to zero. According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for \(x\).

1. Set the first factor equal to zero:
\[ 3.5 - 7x = 0 \]

Solve for \(x\):
\[ 3.5 = 7x \]
\[ x = \frac{3.5}{7} \]
\[ x = 0.5 \]

2. Set the second factor equal to zero:
\[ 0.1x + 2.3 = 0 \]

Solve for \(x\):
\[ 0.1x = -2.3 \]
\[ x = \frac{-2.3}{0.1} \]
\[ x = -23 \]

Therefore, the solutions to the equation \((3.5 - 7x)(0.1x + 2.3) = 0\) are:
\[ x = 0.5 \]
\[ x = -23 \]