a) \(\left(x-3\right)\left(x+3\right)=\left(x-2\right)^2-1\)

\(\Leftrightarrow x^2-9=x^2-4x+4-1\)

\(\Leftrightarrow4x=12\)

\(\Leftrightarrow x=3\)

b) \(\left(2x-1\right)^2=\left(2x+5\right)\left(2x-5\right)+2\)

\(\Leftrightarrow4x^2-4x+1=4x^2-25+2\)

\(\Leftrightarrow4x=24\)

\(\Leftrightarrow x=6\)

c) \(\left(x+1\right)^3=x^2\left(x-2\right)+5\left(x^2-1\right)\)

\(\Leftrightarrow x^3+3x^2+3x+1=x^3-2x^2+5x^2-5\)

\(\Leftrightarrow3x=-6\)

\(\Leftrightarrow x=-2\)

d) \(\left(x^2-3x+9\right)\left(x+3\right)=\left(x-2\right)^3+\left(3x-1\right)\left(2x+3\right)\)

\(\Leftrightarrow x^3+3^3=x^3-6x^2+12x-8+6x^2+7x-3\)

\(\Leftrightarrow x^3+27=x^3+19x-11\)

\(\Leftrightarrow19x=38\)

\(\Leftrightarrow x=2\)