Solve -x^2-ax^2+ax+2x-1=0

$$- x ^ { 2 } - a x ^ { 2 } + a x + 2 x - 1 = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}-ax^{2}+ax-1=-2x$$

Add 1 to both sides.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Add x^{2} to both sides.

$$-ax^{2}+ax=-2x+1+x^{2}$$

Combine all terms containing a.

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

The equation is in standard form.

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

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

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

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

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

Divide \left(x-1\right)^{2} by -x^{2}+x.

$$a=-1+\frac{1}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}-ax^{2}+ax-1=-2x$$

Add 1 to both sides.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Add x^{2} to both sides.

$$-ax^{2}+ax=-2x+1+x^{2}$$

Combine all terms containing a.

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

The equation is in standard form.

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

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

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

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

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

Divide \left(x-1\right)^{2} by -x^{2}+x.

$$a=-1+\frac{1}{x}$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=\frac{1}{a+1}\text{, }&a\neq -1\end{matrix}\right.$$