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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=1-b\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&b=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2x from both sides.

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

Combine 3x and -2x to get x.

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

Add 3xb to both sides.

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

Combine -2xb and 3xb to get xb.

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

Add 1 to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+b.

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

Dividing by 1+b undoes the multiplication by 1+b.

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

Divide -b^{2}+1 by 1+b.

$$x=1-b$$

Solve for x

$$\left\{\begin{matrix}\\x=1-b\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&b=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2x from both sides.

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

Combine 3x and -2x to get x.

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

Add 3xb to both sides.

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

Combine -2xb and 3xb to get xb.

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

Add 1 to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+b.

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

Dividing by 1+b undoes the multiplication by 1+b.

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

Divide -b^{2}+1 by 1+b.

$$x=1-b$$

Solve for b

$$b=-1$$

$$b=1-x$$