Question

(2x-3)(3x-4)-(3x+1)(x-2)-12x+31=0

Answer 1

$(2x-3)(3x-4)-(3x+1)(x-2)-12x+31=0\\\\\\6x^2-8x-9x+12-(3x^2-6x+x-2)-12x+31=0\\\\\\6x^2-8x-9x+12-3x^2+5x+2-12x+31=0\\\\\\3x^2-24x+45=0\;\;\;|\div3\\\\\\x^2-8x+15=0\\\\\\D=(-8)^2-4\cdot1\cdot15=64-60=4\\\\\\x_{1}=\dfrac{8-2}{2}=\dfrac{6}{2}=3\\\\\\x_2=\dfrac{8+2}{2}=\dfrac{10}{2}=5\\\\\\Otvet:\;x_1=3;\;x_2=5.$