Find the Roots (Zeros) 2x^2+x

$2 x^{2} + x$

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

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

Solve for $x$ .

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

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

$x (2 x) + x = 0$

Raise $x$ to the power of $1$ .

$x (2 x) + x = 0$

Factor $x$ out of $x^{1}$ .

$x (2 x) + x \cdot 1 = 0$

Factor $x$ out of $x (2 x) + x \cdot 1$ .

$x (2 x + 1) = 0$

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

$x = 0$

$2 x + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

The final solution is all the values that make $x (2 x + 1) = 0$ true.

$x = 0, - \frac{1}{2}$