\(\Leftrightarrow\left(x^2-x+3\right)\left(x+2\right)=-6x\left(x^2+x+1\right)+7\left(x+2\right)\left(x^2+x+1\right)\)
\(\Leftrightarrow x^3+x^2+x+6=-6x^3-6x^2-6x+7\left(x^3+x^2+x+2x^2+2x+2\right)\)
\(\Leftrightarrow7x^3+7x^2+7x+6=7\left(x^3+3x^2+3x+2\right)\)
=>7x^3+7x^2+7x+6=7x^3+21x^2+21x+14
=>21x^2+21x+14=7x^2+7x+6
=>14x^2+14x+8=0
=>\(x\in\varnothing\)