Solve x(3-2p)-1=x(2-3b)-b^2

$$x ( 3 - 2 p ) - 1 = x ( 2 - 3 b ) - b ^ { 2 }$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{3bx+x+b^{2}-1}{2x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&\left(b=-1\text{ or }b=1\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3-2p.

$$3x-2xp-1=x\left(2-3b\right)-b^{2}$$

Use the distributive property to multiply x by 2-3b.

$$3x-2xp-1=2x-3xb-b^{2}$$

Subtract 3x from both sides.

$$-2xp-1=2x-3xb-b^{2}-3x$$

Combine 2x and -3x to get -x.

$$-2xp-1=-x-3xb-b^{2}$$

Add 1 to both sides.

$$-2xp=-x-3xb-b^{2}+1$$

The equation is in standard form.

$$\left(-2x\right)p=1-b^{2}-x-3bx$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)p}{-2x}=\frac{1-b^{2}-x-3bx}{-2x}$$

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

$$p=\frac{1-b^{2}-x-3bx}{-2x}$$

Divide -x-3xb-b^{2}+1 by -2x.

$$p=\frac{b^{2}-1}{2x}+\frac{3b}{2}+\frac{1}{2}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{3bx+x+b^{2}-1}{2x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }|b|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3-2p.

$$3x-2xp-1=x\left(2-3b\right)-b^{2}$$

Use the distributive property to multiply x by 2-3b.

$$3x-2xp-1=2x-3xb-b^{2}$$

Subtract 3x from both sides.

$$-2xp-1=2x-3xb-b^{2}-3x$$

Combine 2x and -3x to get -x.

$$-2xp-1=-x-3xb-b^{2}$$

Add 1 to both sides.

$$-2xp=-x-3xb-b^{2}+1$$

The equation is in standard form.

$$\left(-2x\right)p=1-b^{2}-x-3bx$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)p}{-2x}=\frac{1-b^{2}-x-3bx}{-2x}$$

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

$$p=\frac{1-b^{2}-x-3bx}{-2x}$$

Divide -x-3xb-b^{2}+1 by -2x.

$$p=\frac{b^{2}-1}{2x}+\frac{3b}{2}+\frac{1}{2}$$

Solve for b (complex solution)

$$b=\frac{\sqrt{9x^{2}+8px-4x+4}-3x}{2}$$

$$b=\frac{-\sqrt{9x^{2}+8px-4x+4}-3x}{2}$$

Solve for b

$$b=\frac{\sqrt{9x^{2}+8px-4x+4}-3x}{2}$$

$$b=\frac{-\sqrt{9x^{2}+8px-4x+4}-3x}{2}\text{, }\left(p>-1\text{ and }p<2\right)\text{ or }x\geq \frac{2\sqrt{\left(2p-1\right)^{2}-9}-4p+2}{9}\text{ or }x\leq \frac{-2\sqrt{\left(2p-1\right)^{2}-9}-4p+2}{9}\text{ or }\left(p\geq -1\text{ and }p\leq 2\right)$$