Solve by Factoring x^2-x-6=-6-7x

$x^{2} - x - 6 = - 6 - 7 x$

Step 1

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

Add $6$ to both sides of the equation.

$x^{2} - x - 6 + 6 = - 7 x$

Add $7 x$ to both sides of the equation.

$x^{2} - x - 6 + 6 + 7 x = 0$

Step 2

Simplify $x^{2} - x - 6 + 6 + 7 x$ .

Combine the opposite terms in $x^{2} - x - 6 + 6 + 7 x$ .

Add $- 6$ and $6$ .

$x^{2} - x + 0 + 7 x = 0$

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

$x^{2} - x + 7 x = 0$

Add $- x$ and $7 x$ .

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

Step 3

Factor $x$ out of $x^{2} + 6 x$ .

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

$x \cdot x + 6 x = 0$

Factor $x$ out of $6 x$ .

$x \cdot x + x \cdot 6 = 0$

Factor $x$ out of $x \cdot x + x \cdot 6$ .

$x (x + 6) = 0$

Step 4

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

$x = 0$

$x + 6 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 7

The final solution is all the values that make $x (x + 6) = 0$ true.

$x = 0, - 6$