\(\left(x+3\right)\left(x-1\right)-\left(4x+3\right)^2=9\\ \Leftrightarrow x^2+2x-3-16x^2-24x-9=9\\ \Leftrightarrow-15x^2-22x-21=0\\ \Leftrightarrow-15\left(x^2+\dfrac{22}{15}x+\dfrac{21}{15}\right)=0\\ \Leftrightarrow-15\left(x^2+2\cdot\dfrac{11}{15}x+\dfrac{121}{225}-\dfrac{121}{225}+\dfrac{21}{15}\right)=0\\ \Leftrightarrow-15\left[\left(x+\dfrac{11}{15}\right)^2+\dfrac{194}{225}\right]=0\\ \Leftrightarrow-15\left(x+\dfrac{11}{15}\right)^2-\dfrac{194}{15}=0\\ \Leftrightarrow x\in\varnothing\left[-15\left(x+\dfrac{11}{15}\right)^2-\dfrac{194}{15}\le-\dfrac{194}{15}< 0\right]\)
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