Question

(4x-9) (x-2) -(1-x) (2-x) =0​

Answer 1

$\displaystyle (4x-9)(x-2)-(1-x)(2-x)=0\\(4x-9)(x-2)+(-1+x)(-(x-2))=0\\(x-2)(4x-9-(-1+x))=0\\(x-2)(4x-9+1-x)=0\\(x-2)(3x-8)=0\\x-2=0,3x-8=0\\\\x_1=2,x_2=\frac{8}{3}$

Answer 2

$\displaystyle\bf\\(4x-9)(x-2)-(1-x)(2-x)=0\\\\(4x-9)(x-2)+(1-x)(x-2)=0\\\\(x-2)(4x-9+1-x)=0\\\\(x-2)(3x-8)=0\\\\\\\left[\begin{array}{ccc}x-2=0\\3x-8=0\end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1} =2\\x_{2} =2\dfrac{2}{3} \end{array}\right\\\\\\Otvet:2 \ ; \ 2\frac{2}{3}$