Solve for x -x^2+10x=x^2-6x

$- x^{2} + 10 x = x^{2} - 6 x$

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

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

$- x^{2} + 10 x - x^{2} = - 6 x$

Add $6 x$ to both sides of the equation.

$- x^{2} + 10 x - x^{2} + 6 x = 0$

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

$- 2 x^{2} + 10 x + 6 x = 0$

Add $10 x$ and $6 x$ .

$- 2 x^{2} + 16 x = 0$

Factor $- 2 x$ out of $- 2 x^{2} + 16 x$ .

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

$- 2 x \cdot x + 16 x = 0$

Factor $- 2 x$ out of $16 x$ .

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

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

$- 2 x (x - 8) = 0$

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

$x = 0$

$x - 8 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

The final solution is all the values that make $- 2 x (x - 8) = 0$ true.

$x = 0, 8$