To solve the equation \((4x^2 - 1)(1.8 - 2x) = 0\), we need to find the values of \(x\) that make the product equal to zero. This can be done by setting each factor equal to zero and solving for \(x\).

### Step 1: Solve \(4x^2 - 1 = 0\)

1. \(4x^2 - 1 = 0\)
2. Add 1 to both sides:
\[
4x^2 = 1
\]
3. Divide both sides by 4:
\[
x^2 = \frac{1}{4}
\]
4. Take the square root of both sides:
\[
x = \pm \frac{1}{2}
\]

So, the solutions from this factor are \(x = \frac{1}{2}\) and \(x = -\frac{1}{2}\).

### Step 2: Solve \(1.8 - 2x = 0\)

1. \(1.8 - 2x = 0\)
2. Add \(2x\) to both sides:
\[
1.8 = 2x
\]
3. Divide both sides by 2:
\[
x = \frac{1.8}{2} = 0.9
\]

So, the solution from this factor is \(x = 0.9\).

### Conclusion

The solutions to the equation \((4x^2 - 1)(1.8 - 2x) = 0\) are:
\[
x = \frac{1}{2}, \quad x = -\frac{1}{2}, \quad \text{and} \quad x = 0.9
\]