Solve by Factoring 14x^2=-21x

$14 x^{2} = - 21 x$

Step 1

Add $21 x$ to both sides of the equation.

$14 x^{2} + 21 x = 0$

Step 2

Factor $7 x$ out of $14 x^{2} + 21 x$ .

Factor $7 x$ out of $14 x^{2}$ .

$7 x (2 x) + 21 x = 0$

Factor $7 x$ out of $21 x$ .

$7 x (2 x) + 7 x (3) = 0$

Factor $7 x$ out of $7 x (2 x) + 7 x (3)$ .

$7 x (2 x + 3) = 0$

Step 3

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

$x = 0$

$2 x + 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

Step 6

The final solution is all the values that make $7 x (2 x + 3) = 0$ true.

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