Solve for x -x^2+6x=x^2-2x

$- x^{2} + 6 x = x^{2} - 2 x$

Step 1

Move all terms containing $x$ to the left side of the equation.

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

$- x^{2} + 6 x - x^{2} = - 2 x$

Add $2 x$ to both sides of the equation.

$- x^{2} + 6 x - x^{2} + 2 x = 0$

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

$- 2 x^{2} + 6 x + 2 x = 0$

Add $6 x$ and $2 x$ .

$- 2 x^{2} + 8 x = 0$

Step 2

Factor $- 2 x$ out of $- 2 x^{2} + 8 x$ .

Factor $- 2 x$ out of $- 2 x^{2}$ .

$- 2 x \cdot x + 8 x = 0$

Factor $- 2 x$ out of $8 x$ .

$- 2 x \cdot x - 2 x \cdot - 4 = 0$

Factor $- 2 x$ out of $- 2 x (x) - 2 x (- 4)$ .

$- 2 x (x - 4) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 4 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 6

The final solution is all the values that make $- 2 x (x - 4) = 0$ true.

$x = 0, 4$