Solve mx^2+6m=5mx-1

$$m x ^ { 2 } + 6 m = 5 m x - 1$$

Solve for m

$$m=-\frac{1}{\left(x-3\right)\left(x-2\right)}$$

$$x\neq 2\text{ and }x\neq 3$$

Steps for Solving Linear Equation

Subtract 5mx from both sides.

$$mx^{2}+6m-5mx=-1$$

Combine all terms containing m.

$$\left(x^{2}+6-5x\right)m=-1$$

The equation is in standard form.

$$\left(x^{2}-5x+6\right)m=-1$$

Divide both sides by x^{2}-5x+6.

$$\frac{\left(x^{2}-5x+6\right)m}{x^{2}-5x+6}=-\frac{1}{x^{2}-5x+6}$$

Dividing by x^{2}-5x+6 undoes the multiplication by x^{2}-5x+6.

$$m=-\frac{1}{x^{2}-5x+6}$$

Divide -1 by x^{2}-5x+6.

$$m=-\frac{1}{\left(x-3\right)\left(x-2\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-4m}}{2m}+\frac{5}{2}$$

$$x=-\frac{\sqrt{m^{2}-4m}}{2m}+\frac{5}{2}\text{, }m\neq 0$$

Solve for x

$$x=\frac{\sqrt{m^{2}-4m}}{2m}+\frac{5}{2}$$

$$x=-\frac{\sqrt{m^{2}-4m}}{2m}+\frac{5}{2}\text{, }m<0\text{ or }m\geq 4$$