Question

9x^2-16-x.(3x-4)=0

Answer 1

Answer 2

\(9x^2-16-x\left(3x-4\right)=0\)

\(\Leftrightarrow\left[\left(3x\right)^2-4^2\right]-x\left(3x-4\right)=0\)

\(\Leftrightarrow\left(3x-4\right)\left(3x+4\right)-x\left(3x-4\right)=0\)

\(\Leftrightarrow\left(3x-4\right)\left(3x+4-x\right)=0\)

\(\Leftrightarrow\left(3x-4\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-4=0\\2x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x_1=\dfrac{4}{3}\\x_2=-2\end{matrix}\right.\)