\(\Leftrightarrow\left(x+1\right)\left(x+4\right)\left(9x^2+24x+6x+16\right)=4x^2\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)\left(3x+8\right)\left(3x+2\right)=4x^2\)
\(\Leftrightarrow\left(3x+8\right)\left(x+1\right)\left(3x+2\right)\left(x+4\right)=4x^2\)
\(\Leftrightarrow\left(3x^2+3x+8x+8\right)\left(3x^2+12x+2x+8\right)=4x^2\)
\(\Leftrightarrow\left(3x^2+11x+8\right)\left(3x^2+14x+8\right)=4x^2\)
\(\Leftrightarrow\left(3x^2+8\right)^2+25x\left(3x^2+8\right)+154x^2-4x^2=0\)
\(\Leftrightarrow\left(3x^2+8\right)^2+25x\left(3x^2+8\right)+150x^2=0\)
\(\Leftrightarrow\left(3x^2+8\right)^2+10x\left(3x^2+8\right)+15x\left(3x^2+8\right)+150x^2=0\)
\(\Leftrightarrow\left(3x^2+8\right)\left(3x^2+10x+8\right)+15x\left(3x^2+10x+8\right)=0\)
\(\Leftrightarrow\left(3x^2+10x+8\right)\left(3x^2+15x+8\right)=0\)
\(\Leftrightarrow x\in\left\{\dfrac{-15+\sqrt{129}}{6};\dfrac{-15-\sqrt{129}}{6};-\dfrac{4}{3};-2\right\}\)
