Solve (m+6)x^2+(m+6)x+2=0

$$( m + 6 ) x ^ { 2 } + ( m + 6 ) x + 2 = 0$$

Solve for m

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

$$x\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+6 by x^{2}.

$$mx^{2}+6x^{2}+\left(m+6\right)x+2=0$$

Use the distributive property to multiply m+6 by x.

$$mx^{2}+6x^{2}+mx+6x+2=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Subtract 6x from both sides.

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

Subtract 2 from both sides.

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

Combine all terms containing m.

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

Divide both sides by x^{2}+x.

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

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

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

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

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

Solve for x (complex solution)

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

$$x=-\frac{\sqrt{\left(m-2\right)\left(m+6\right)}+m+6}{2\left(m+6\right)}\text{, }m\neq -6$$

Solve for x

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

$$x=-\frac{\sqrt{\left(m-2\right)\left(m+6\right)}+m+6}{2\left(m+6\right)}\text{, }m\geq 2\text{ or }m<-6$$