[tex]2x^2-\left(m-1\right)x+3=0\\\\2x^2-\left(m-1\right)x+3-2x^2=0-2x^2\\\\-\left(m-1\right)x+3=-2x^2\\\\-\left(m-1\right)x+3-3=-2x^2-3\\\\-\left(m-1\right)x=-2x^2-3\\\\\frac{-\left(m-1\right)x}{-x}=-\frac{2x^2}{-x}-\frac{3}{-x};\quad \:x\ne \:0\\\\m-1=-\frac{-2x^2-3}{x};\quad \:x\ne \:0\\\\m-1+1=-\frac{-2x^2-3}{x}+1;\quad \:x\ne \:0\\\\m=-\frac{-2x^2-3}{x}+1;\quad \:x\ne \:0[/tex]
