Solve for x 4x^2+12x=0

$4 x^{2} + 12 x = 0$

Step 1

Factor $4 x$ out of $4 x^{2} + 12 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) + 12 x = 0$

Factor $4 x$ out of $12 x$ .

$4 x (x) + 4 x (3) = 0$

Factor $4 x$ out of $4 x (x) + 4 x (3)$ .

$4 x (x + 3) = 0$

Step 2

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

$x = 0$

$x + 3 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 5

The final solution is all the values that make $4 x (x + 3) = 0$ true.

$x = 0, - 3$