Solve 2x^2+(m-7)x+(-2m+2)=0

$$2 x ^ { 2 } + ( m - 7 ) x + ( - 2 m + 2 ) = 0$$

Solve for m

$$m=-\frac{2x^{2}-7x+2}{x-2}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-7 by x.

$$2x^{2}+mx-7x-2m+2=0$$

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx-7x-2m+2=-2x^{2}$$

Add 7x to both sides.

$$mx-2m+2=-2x^{2}+7x$$

Subtract 2 from both sides.

$$mx-2m=-2x^{2}+7x-2$$

Combine all terms containing m.

$$\left(x-2\right)m=-2x^{2}+7x-2$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)m}{x-2}=\frac{-2x^{2}+7x-2}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$m=\frac{-2x^{2}+7x-2}{x-2}$$

Solve for x

$$x=\frac{\sqrt{m^{2}+2m+33}-m+7}{4}$$

$$x=\frac{-\sqrt{m^{2}+2m+33}-m+7}{4}$$