Solve by Factoring x^2-5x=2x^2-5x

$x^{2} - 5 x = 2 x^{2} - 5 x$

Move all the expressions to the left side of the equation.

Subtract $2 x^{2}$ from both sides of the equation.

$x^{2} - 5 x - 2 x^{2} = - 5 x$

Add $5 x$ to both sides of the equation.

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

Simplify $x^{2} - 5 x - 2 x^{2} + 5 x$ .

Combine the opposite terms in $x^{2} - 5 x - 2 x^{2} + 5 x$ .

Add $- 5 x$ and $5 x$ .

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

Add $x^{2} - 2 x^{2}$ and $0$ .

$x^{2} - 2 x^{2} = 0$

Subtract $2 x^{2}$ from $x^{2}$ .

$- x^{2} = 0$

Divide each term in $- x^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- x^{2} = 0$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{0}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$