Solve (m-12)x^2+2(m-12)x+2=0

$$( m - 12 ) x ^ { 2 } + 2 ( m - 12 ) x + 2 = 0$$

Solve for m

$$m=-\frac{2\left(1-12x-6x^{2}\right)}{x\left(x+2\right)}$$

$$x\neq -2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-12 by x^{2}.

$$mx^{2}-12x^{2}+2\left(m-12\right)x+2=0$$

Use the distributive property to multiply 2 by m-12.

$$mx^{2}-12x^{2}+\left(2m-24\right)x+2=0$$

Use the distributive property to multiply 2m-24 by x.

$$mx^{2}-12x^{2}+2mx-24x+2=0$$

Add 12x^{2} to both sides. Anything plus zero gives itself.

$$mx^{2}+2mx-24x+2=12x^{2}$$

Add 24x to both sides.

$$mx^{2}+2mx+2=12x^{2}+24x$$

Subtract 2 from both sides.

$$mx^{2}+2mx=12x^{2}+24x-2$$

Combine all terms containing m.

$$\left(x^{2}+2x\right)m=12x^{2}+24x-2$$

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

$$\frac{\left(x^{2}+2x\right)m}{x^{2}+2x}=\frac{12x^{2}+24x-2}{x^{2}+2x}$$

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

$$m=\frac{12x^{2}+24x-2}{x^{2}+2x}$$

Divide 12x^{2}+24x-2 by x^{2}+2x.

$$m=\frac{2\left(6x^{2}+12x-1\right)}{x\left(x+2\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(m-14\right)\left(m-12\right)}-m+12}{m-12}$$

$$x=\frac{-\sqrt{\left(m-14\right)\left(m-12\right)}-m+12}{m-12}\text{, }m\neq 12$$

Solve for x

$$x=\frac{\sqrt{\left(m-14\right)\left(m-12\right)}-m+12}{m-12}$$

$$x=\frac{-\sqrt{\left(m-14\right)\left(m-12\right)}-m+12}{m-12}\text{, }m\geq 14\text{ or }m<12$$