Solve (2x-6)=2x^2+mx-18

$$( 2 x - 6 ) = 2 x ^ { 2 } + m x - 18$$

Solve for m

$$m=-2x+2+\frac{12}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}+mx-18=2x-6$$

Subtract 2x^{2} from both sides.

$$mx-18=2x-6-2x^{2}$$

Add 18 to both sides.

$$mx=2x-6-2x^{2}+18$$

Add -6 and 18 to get 12.

$$mx=2x+12-2x^{2}$$

The equation is in standard form.

$$xm=12+2x-2x^{2}$$

Divide both sides by x.

$$\frac{xm}{x}=-\frac{2\left(x-3\right)\left(x+2\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$m=-\frac{2\left(x-3\right)\left(x+2\right)}{x}$$

Divide -2\left(-3+x\right)\left(2+x\right) by x.

$$m=-2x+2+\frac{12}{x}$$

Solve for x

$$x=-\frac{\sqrt{m^{2}-4m+100}}{4}-\frac{m}{4}+\frac{1}{2}$$

$$x=\frac{\sqrt{m^{2}-4m+100}}{4}-\frac{m}{4}+\frac{1}{2}$$