Question

(2x-3)² - 4x(x+1)=12

x² - 4 +3x (x-2)=0

Answer 1

\(\left(2x-3\right)^2-4x\left(x+1\right)=12\\ \Leftrightarrow4x^2-12x+9-4x^2-4x-12=0\\ \Leftrightarrow-16x-3=0\\ \Leftrightarrow x=-\dfrac{3}{16}\)

\(x^2-4+3x\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)+3x\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2+3x\right)=0\\ \Leftrightarrow\left(x-2\right)\left(4x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{2}{4}=-\dfrac{1}{2}\end{matrix}\right.\)