Solve by Factoring x^2+6x+4=-2x+4

$x^{2} + 6 x + 4 = - 2 x + 4$

Step 1

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

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

$x^{2} + 6 x + 4 + 2 x = 4$

Subtract $4$ from both sides of the equation.

$x^{2} + 6 x + 4 + 2 x - 4 = 0$

Step 2

Simplify $x^{2} + 6 x + 4 + 2 x - 4$ .

Combine the opposite terms in $x^{2} + 6 x + 4 + 2 x - 4$ .

Subtract $4$ from $4$ .

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

Add $x^{2} + 6 x + 2 x$ and $0$ .

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

Add $6 x$ and $2 x$ .

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

Step 3

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

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

$x \cdot x + 8 x = 0$

Factor $x$ out of $8 x$ .

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

Factor $x$ out of $x \cdot x + x \cdot 8$ .

$x (x + 8) = 0$

Step 4

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

$x = 0$

$x + 8 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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

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

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 7

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

$x = 0, - 8$