Solve x^2+(p+1)x=5-2p

$$x ^ { 2 } + ( p + 1 ) x = 5 - 2 p$$

Solve for p

$$p=-\frac{x^{2}+x-5}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Use the distributive property to multiply p+1 by x.

$$x^{2}+px+x=5-2p$$

Add 2p to both sides.

$$x^{2}+px+x+2p=5$$

Subtract x^{2} from both sides.

$$px+x+2p=5-x^{2}$$

Subtract x from both sides.

$$px+2p=5-x^{2}-x$$

Combine all terms containing p.

$$\left(x+2\right)p=5-x^{2}-x$$

The equation is in standard form.

$$\left(x+2\right)p=5-x-x^{2}$$

Divide both sides by x+2.

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

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

$$p=\frac{5-x-x^{2}}{x+2}$$

Solve for x

$$x=\frac{\sqrt{p^{2}-6p+21}-p-1}{2}$$

$$x=\frac{-\sqrt{p^{2}-6p+21}-p-1}{2}$$