Solve (x-5)(x-a)+2x(2x-2a)=0

$$( x - 5 ) ( x - a ) + 2 x ( 2 x - 2 a ) = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x-5 by x-a.

$$x^{2}-xa-5x+5a+2x\left(2x-2a\right)=0$$

Use the distributive property to multiply 2x by 2x-2a.

$$x^{2}-xa-5x+5a+4x^{2}-4ax=0$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-xa-5x+5a-4ax=0$$

Combine -xa and -4ax to get -5xa.

$$5x^{2}-5xa-5x+5a=0$$

Subtract 5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-5xa-5x+5a=-5x^{2}$$

Add 5x to both sides.

$$-5xa+5a=-5x^{2}+5x$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -5x+5.

$$\frac{\left(5-5x\right)a}{5-5x}=\frac{5x\left(1-x\right)}{5-5x}$$

Dividing by -5x+5 undoes the multiplication by -5x+5.

$$a=\frac{5x\left(1-x\right)}{5-5x}$$

Divide 5x\left(1-x\right) by -5x+5.

$$a=x$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply x-5 by x-a.

$$x^{2}-xa-5x+5a+2x\left(2x-2a\right)=0$$

Use the distributive property to multiply 2x by 2x-2a.

$$x^{2}-xa-5x+5a+4x^{2}-4ax=0$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-xa-5x+5a-4ax=0$$

Combine -xa and -4ax to get -5xa.

$$5x^{2}-5xa-5x+5a=0$$

Subtract 5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-5xa-5x+5a=-5x^{2}$$

Add 5x to both sides.

$$-5xa+5a=-5x^{2}+5x$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -5x+5.

$$\frac{\left(5-5x\right)a}{5-5x}=\frac{5x\left(1-x\right)}{5-5x}$$

Dividing by -5x+5 undoes the multiplication by -5x+5.

$$a=\frac{5x\left(1-x\right)}{5-5x}$$

Divide 5x\left(1-x\right) by -5x+5.

$$a=x$$

Solve for x

$$x=a$$

$$x=1$$