To solve the equation \(-5(4x - 1)(x - 2) = 2(4x - 1)^2\), let's start by expanding both sides of the equation.

First, expand the left-hand side:
\[
-5(4x - 1)(x - 2)
\]

Distribute \(4x - 1\) with \(x - 2\):
\[
(4x - 1)(x - 2) = 4x(x - 2) - 1(x - 2) = 4x^2 - 8x - x + 2 = 4x^2 - 9x + 2
\]

Now multiply by \(-5\):
\[
-5(4x^2 - 9x + 2) = -20x^2 + 45x - 10
\]

Next, expand the right-hand side:
\[
2(4x - 1)^2
\]

First, expand \((4x - 1)^2\):
\[
(4x - 1)^2 = (4x - 1)(4x - 1) = 16x^2 - 8x - 8x + 1 = 16x^2 - 8x + 1
\]

Now multiply by \(2\):
\[
2(16x^2 - 8x + 1) = 32x^2 - 16x + 2
\]

So the equation becomes:
\[
-20x^2 + 45x - 10 = 32x^2 - 16x + 2
\]

Combine like terms by moving everything to one side of the equation:
\[
-20x^2 + 45x - 10 - 32x^2 + 16x - 2 = 0
\]

Combine the terms:
\[
-52x^2 + 61x - 12 = 0
\]

Now we have a quadratic equation:
\[
-52x^2 + 61x - 12 = 0
\]

To solve this quadratic equation, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \(a = -52\), \(b = 61\), and \(c = -12\). Plugging these values into the quadratic formula gives:
\[
x = \frac{-61 \pm \sqrt{61^2 - 4(-52)(-12)}}{2(-52)}
\]

Calculate the discriminant:
\[
61^2 - 4(-52)(-12) = 3721 - 2496 = 1225
\]

So,
\[
x = \frac{-61 \pm \sqrt{1225}}{2(-52)}
\]

Since \(\sqrt{1225} = 35\), we have:
\[
x = \frac{-61 \pm 35}{-104}
\]

This gives us two solutions:
\[
x = \frac{-61 + 35}{-104} = \frac{-26}{-104} = \frac{1}{4}
\]

\[
x = \frac{-61 - 35}{-104} = \frac{-96}{-104} = \frac{24}{26} = \frac{12}{13}
\]

Thus, the solutions to the equation are:
\[
x = \frac{1}{4} \quad \text{and} \quad x = \frac{12}{13}
\]