Solve a^2(x-1)=5(ax-5)

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{a+5}{a}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-1.

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

Use the distributive property to multiply 5 by ax-5.

$$a^{2}x-a^{2}=5ax-25$$

Subtract 5ax from both sides.

$$a^{2}x-a^{2}-5ax=-25$$

Add a^{2} to both sides.

$$a^{2}x-5ax=-25+a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-5a\right)x=-25+a^{2}$$

The equation is in standard form.

$$\left(a^{2}-5a\right)x=a^{2}-25$$

Divide both sides by a^{2}-5a.

$$\frac{\left(a^{2}-5a\right)x}{a^{2}-5a}=\frac{a^{2}-25}{a^{2}-5a}$$

Dividing by a^{2}-5a undoes the multiplication by a^{2}-5a.

$$x=\frac{a^{2}-25}{a^{2}-5a}$$

Divide a^{2}-25 by a^{2}-5a.

$$x=\frac{a+5}{a}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{a+5}{a}\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-1.

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

Use the distributive property to multiply 5 by ax-5.

$$a^{2}x-a^{2}=5ax-25$$

Subtract 5ax from both sides.

$$a^{2}x-a^{2}-5ax=-25$$

Add a^{2} to both sides.

$$a^{2}x-5ax=-25+a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-5a\right)x=-25+a^{2}$$

The equation is in standard form.

$$\left(a^{2}-5a\right)x=a^{2}-25$$

Divide both sides by a^{2}-5a.

$$\frac{\left(a^{2}-5a\right)x}{a^{2}-5a}=\frac{a^{2}-25}{a^{2}-5a}$$

Dividing by a^{2}-5a undoes the multiplication by a^{2}-5a.

$$x=\frac{a^{2}-25}{a^{2}-5a}$$

Divide a^{2}-25 by a^{2}-5a.

$$x=\frac{a+5}{a}$$

Solve for a

$$\left\{\begin{matrix}\\a=5\text{, }&\text{unconditionally}\\a=\frac{5}{x-1}\text{, }&x\neq 1\end{matrix}\right.$$