First, let's expand and simplify each term on the left side of the equation:

$x+2$² = x² + 4x + 4

-x$3x+1$² = -x$9x^2+6x+1$ = -9x³ - 6x² - x

$2x+1$$4x^2-2x+1$ = 8x³ - 4x² + 4x + 4x² - 2x + 1 = 8x³

Now, substitute these results back into the original equation:

x² + 4x + 4 - 9x³ - 6x² - x + 8x³ = 42

Combine like terms:

9x³ - 6x² + x + 4 = 42

Rearrange the terms to set the equation equal to zero:

9x³ - 6x² + x + 4 - 42 = 0

9x³ - 6x² + x - 38 = 0

Therefore, the solution to the equation $x+2$²-x$3x+1$²+$2x+1$$4x^2-2x+1$=42 is 9x³ - 6x² + x - 38 = 0.