\(4x\left(2x-3\right)-2x-3=0\)
\(\Rightarrow4x\left(2x-3\right)-1\left(2x+3\right)=0\)
\(\Rightarrow4x\left(2x-3\right)+1\left(2x-3\right)=0\)
\(\Rightarrow\left(4x+1\right)\left(2x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x+1=0\\2x-3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=\dfrac{3}{2}\end{matrix}\right.\)
\(\left(4x-5\right)\left(6x+1\right)-\left(8x+3\right)\left(3x-4\right)=15\)
\(\Rightarrow\left[4x\left(6x+1\right)-5\left(6x+1\right)\right]-\left[8x\left(3x-4\right)+3\left(3x-4\right)\right]=15\)\(\Rightarrow\left(24x^2+4x-30x-5\right)-\left(24x^2-32x+9x-12\right)=15\)
\(\Rightarrow\left(24x^2-26x-5\right)-\left(24x^2-23x-12\right)=15\)
\(\Rightarrow24x^2-26x-5-24x^2+23x+12=15\)
\(\Rightarrow\left(24x^2-24x^2\right)-\left(26x-23x\right)+\left(12-5\right)=15\)
\(\Rightarrow-3x+7=15\)
\(\Rightarrow-3x=8\Rightarrow x=-\dfrac{8}{3}\)
