a. \(\left(x-1\right)\left(x^2+x+1\right)-x\left(x+2\right)\left(x-2\right)=5\Leftrightarrow x^3-1-x\left(x^2-4\right)=5\Leftrightarrow x^3-1-x^3+4x=5\Leftrightarrow4x-1=5\Leftrightarrow4x=6\Leftrightarrow x=\dfrac{3}{2}\)
b. \(\left(6x-2\right)^2+\left(5x-2\right)^2-4\left(3x-1\right)\left(5x-2\right)=0\Leftrightarrow36x^2-24x+4+25x^2-20x+4-4\left(15x^2-6x-5x+2\right)=0\Leftrightarrow36x^2-24x+4+25x^2-20x+4-60x^2+24x+20x-8=0\Leftrightarrow x^2=0\Leftrightarrow x=0\)
c. \(\left(x+1\right)^3-x\left(x-2\right)^2+x-1=0\Leftrightarrow x^3+3x^2+3x+1-x\left(x^2-4x+4\right)+x-1=0\Leftrightarrow x^3+3x^2+3x+1-x^3+4x^2-4x+x-1=0\Leftrightarrow7x^2=0\Leftrightarrow x=0\)