Solve 3mx^2-3mx-6m+15=0

$$3 m x ^ { 2 } - 3 m x - 6 m + 15 = 0$$

Solve for m

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

$$x\neq -1\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$3mx^{2}-3mx-6m=-15$$

Combine all terms containing m.

$$\left(3x^{2}-3x-6\right)m=-15$$

Divide both sides by 3x^{2}-3x-6.

$$\frac{\left(3x^{2}-3x-6\right)m}{3x^{2}-3x-6}=-\frac{15}{3x^{2}-3x-6}$$

Dividing by 3x^{2}-3x-6 undoes the multiplication by 3x^{2}-3x-6.

$$m=-\frac{15}{3x^{2}-3x-6}$$

Divide -15 by 3x^{2}-3x-6.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{m\left(9m-20\right)}+m}{2m}$$

$$x=\frac{-\sqrt{m\left(9m-20\right)}+m}{2m}\text{, }m\neq 0$$

Solve for x

$$x=\frac{\sqrt{m\left(9m-20\right)}+m}{2m}$$

$$x=\frac{-\sqrt{m\left(9m-20\right)}+m}{2m}\text{, }m<0\text{ or }m\geq \frac{20}{9}$$