Solve for x 3x=-x^2

$3 x = - x^{2}$

Step 1

Add $x^{2}$ to both sides of the equation.

$3 x + x^{2} = 0$

Step 2

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$3 u + u^{2} = 0$

Factor $u$ out of $3 u + u^{2}$ .

Factor $u$ out of $3 u$ .

$u \cdot 3 + u^{2} = 0$

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

$u \cdot 3 + u \cdot u = 0$

Factor $u$ out of $u \cdot 3 + u \cdot u$ .

$u (3 + u) = 0$

Replace all occurrences of $u$ with $x$ .

$x (3 + x) = 0$

Step 3

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

$x = 0$

$3 + x = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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

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

$3 + x = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

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

$x = 0, - 3$