To solve the equation \(-2x(x-3) - (x-1)(2-x) = -1 - x^2\), let's start by expanding and simplifying both sides of the equation.

First, expand the left-hand side:

\[
-2x(x-3) - (x-1)(2-x)
\]

Expand \(-2x(x-3)\):

\[
-2x^2 + 6x
\]

Next, expand \((x-1)(2-x)\):

\[
(x-1)(2-x) = x(2-x) - 1(2-x) = 2x - x^2 - 2 + x = -x^2 + 3x - 2
\]

So, the left-hand side becomes:

\[
-2x^2 + 6x - (-x^2 + 3x - 2)
\]

Distribute the negative sign:

\[
-2x^2 + 6x + x^2 - 3x + 2
\]

Combine like terms:

\[
-2x^2 + x^2 + 6x - 3x + 2 = -x^2 + 3x + 2
\]

Now, the equation is:

\[
-x^2 + 3x + 2 = -1 - x^2
\]

Next, let's move all terms to one side of the equation to set it to zero. Add \(x^2\) to both sides and subtract \(3x + 2\) from both sides:

\[
-x^2 + 3x + 2 + x^2 - 3x - 2 = -1 - x^2 + x^2
\]

Simplify:

\[
0 = -1
\]

This is a contradiction, which means there are no solutions to the equation. Therefore, the original equation \(-2x(x-3) - (x-1)(2-x) = -1 - x^2\) has no solutions.