Solve 9x^2+2px=2-p

$$9 x ^ { 2 } + 2 p x = 2 - p$$

Solve for p

$$p=-\frac{9x^{2}-2}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Add p to both sides.

$$9x^{2}+2px+p=2$$

Subtract 9x^{2} from both sides.

$$2px+p=2-9x^{2}$$

Combine all terms containing p.

$$\left(2x+1\right)p=2-9x^{2}$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)p}{2x+1}=\frac{2-9x^{2}}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$p=\frac{2-9x^{2}}{2x+1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(p-6\right)\left(p-3\right)}-p}{9}$$

$$x=\frac{-\sqrt{\left(p-6\right)\left(p-3\right)}-p}{9}$$

Solve for x

$$x=\frac{\sqrt{\left(p-6\right)\left(p-3\right)}-p}{9}$$

$$x=\frac{-\sqrt{\left(p-6\right)\left(p-3\right)}-p}{9}\text{, }p\leq 3\text{ or }p\geq 6$$