Solve by Factoring 6x^2+2x=0

$6 x^{2} + 2 x = 0$

Step 1

Factor $2 x$ out of $6 x^{2} + 2 x$ .

Factor $2 x$ out of $6 x^{2}$ .

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

Factor $2 x$ out of $2 x$ .

$2 x (3 x) + 2 x (1) = 0$

Factor $2 x$ out of $2 x (3 x) + 2 x (1)$ .

$2 x (3 x + 1) = 0$

Step 2

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

$x = 0$

$3 x + 1 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $3 x + 1$ equal to $0$ and solve for $x$ .

Set $3 x + 1$ equal to $0$ .

$3 x + 1 = 0$

Solve $3 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 5

The final solution is all the values that make $2 x (3 x + 1) = 0$ true.

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