a.
\(x\left(x-3\right)-\left(x-2\right)\left(x+2\right)=-5\left(x+1\right)\)
\(\Leftrightarrow x^2-3x-\left(x^2-4\right)=-5x-5\)
\(\Leftrightarrow x^2-3x-x^2+4=-5x-5\)
\(\Leftrightarrow2x=-9\)
\(\Leftrightarrow x=-\dfrac{9}{2}\)
b.
\(7x\left(x-4\right)-x+4=0\)
\(\Leftrightarrow7x\left(x-4\right)-\left(x-4\right)=0\)
\(\Leftrightarrow\left(7x-1\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}7x-1=0\\x-4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}\\x=4\end{matrix}\right.\)
c.
\(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)=28\)
\(\Leftrightarrow x^3+9x^2+27x+27-x\left(9x^2+6x+1\right)+8x^3+1=28\)
\(\Leftrightarrow x^3+9x^2+27x+27-9x^3-6x^2-x+8x^3+1=28\)
\(\Leftrightarrow3x^2+26x=0\)
\(\Leftrightarrow x\left(3x+26\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{26}{3}\end{matrix}\right.\)
