Solve for x x(2x+7)=0

$x (2 x + 7) = 0$

Step 1

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

$x = 0$

$2 x + 7 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 4

The final solution is all the values that make $x (2 x + 7) = 0$ true.

$x = 0, - \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{7}{2}$

Decimal Form:

$x = 0, - 3.5$

Mixed Number Form:

$x = 0, - 3 \frac{1}{2}$