Solve by Factoring 6x^2-2x=x

$6 x^{2} - 2 x = x$

Step 1

Subtract $x$ from both sides of the equation.

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

Step 2

Subtract $x$ from $- 2 x$ .

$6 x^{2} - 3 x = 0$

Step 3

Factor $3 x$ out of $6 x^{2} - 3 x$ .

Factor $3 x$ out of $6 x^{2}$ .

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

Factor $3 x$ out of $- 3 x$ .

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

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

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

Step 4

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

$x = 0$

$2 x - 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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 $x$ .

Add $1$ to 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 $1$ .

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

Step 7

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

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