\(\left(4x+3\right)\left(x^2-9\right)=\left(x+3\right)\left(16x^2-9\right)\\ \left(4x+3\right)\left(x-3\right)\left(x+3\right)=\left(x+3\right)\left(4x-3\right)\left(4x+3\right)\\ \left(4x+3\right)\left(x-3\right)\left(x+3\right)-\left(x+3\right)\left(4x-3\right)\left(4x+3\right)=0\)
\(\left(4x+3\right)\left(x+3\right)\left(x-3-4x+3\right)=0\\ \left(4x+3\right)\left(x+3\right)\cdot\left(-3x\right)=0\\ \left[{}\begin{matrix}4x+3=0< =>x=-\dfrac{3}{4}\\x+3=0< =>x=-3\\-3x=0< =>x=0\end{matrix}\right.\)
=>(4x+3)(x-3)(x+3)-(x+3)(4x-3)(4x+3)=0
=>(4x+3)(x+3)(x-3-4x+3)=0
=>-3x(4x+3)(x+3)=0
=>\(x\in\left\{0;-\dfrac{3}{4};-3\right\}\)
\(\left(4x+3\right)\left(x^2-9\right)=\left(x+3\right)\left(16x^2-9\right)\)
\(\Leftrightarrow\left(4x+3\right)\left(x-3\right)\left(x+3\right)=\left(x+3\right)\left(4x-3\right)\left(4x+3\right)\)
\(\Leftrightarrow\left(4x+3\right)\left(x-3\right)\left(x+3\right)-\left(x+3\right)\left(4x-3\right)\left(4x+3\right)=0\)
\(\Leftrightarrow\left(4x+3\right)\left(x+3\right)\left(x-3-4x+3\right)=0\)
\(\Leftrightarrow\left(4x+3\right)\left(x+3\right)\left(-3x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x+3=0\\x+3=0\\-3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=-3\\x=0\end{matrix}\right.\)
