Solve for x x^2+8x=-x

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

Step 1

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

Add $x$ to both sides of the equation.

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

Add $8 x$ and $x$ .

$x^{2} + 9 x = 0$

Step 2

Factor $x$ out of $x^{2} + 9 x$ .

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

$x \cdot x + 9 x = 0$

Factor $x$ out of $9 x$ .

$x \cdot x + x \cdot 9 = 0$

Factor $x$ out of $x \cdot x + x \cdot 9$ .

$x (x + 9) = 0$

Step 3

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

$x = 0$

$x + 9 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 6

The final solution is all the values that make $x (x + 9) = 0$ true.

$x = 0, - 9$