Find the Roots (Zeros) y=x^2+3x

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

Step 1

Set $x^{2} + 3 x$ equal to $0$ .

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

Step 2

Solve for $x$ .

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

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

$x \cdot x + 3 x = 0$

Factor $x$ out of $3 x$ .

$x \cdot x + x \cdot 3 = 0$

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

$x (x + 3) = 0$

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

$x = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

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.

$x = - 3$

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

$x = 0, - 3$

Step 3