X9x-5)(x+5) - (x-2)9x2 +2x+40 =3

To solve the equation

\[
(x^9 - 5)(x + 5) - (x - 2)9x^2 + 2x + 40 = 3,
\]

let's first simplify the equation step by step.

1. Rearranging the equation gives us:

\[
(x^9 - 5)(x + 5) - (x - 2)9x^2 + 2x + 40 - 3 = 0.
\]

This simplifies to:

\[
(x^9 - 5)(x + 5) - (x - 2)9x^2 + 2x + 37 = 0.
\]

2. Now, we can expand and simplify further.

Let's first expand \((x^9 - 5)(x + 5)\):

\[
(x^9 - 5)(x + 5) = x^{10} + 5x^9 - 5x - 25.
\]

Next, let's expand \(-(x - 2)9x^2\):

\[
-(x - 2)9x^2 = -9x^3 + 18x^2.
\]

Now plugging these expansions back into the equation we have:

\[
(x^{10} + 5x^9 - 5x - 25) + (-9x^3 + 18x^2) + 2x + 37 = 0.
\]

Combining like terms yields:

\[
x^{10} + 5x^9 - 9x^3 + 18x^2 - 3x + 12 = 0.
\]

Now we have a polynomial equation:

\[
x^{10} + 5x^9 - 9x^3 + 18x^2 - 3x + 12 = 0.
\]

This equation might be difficult to factor or solve analytically due to the degree of the polynomial. You can use numerical methods or graphing techniques to find the roots, or use software tools or a calculator designed for polynomial equations.

If you're looking for integer or rational roots, you might try the Rational Root Theorem, testing factors of the constant term (12) against the leading coefficient (1).

However, given the complexity of this polynomial, the best approach would be either numerical approximations or software tools that can handle polynomial equations.