Solve for x (3x^2-2)/x=(6x-2)/x

$\frac{3 x^{2} - 2}{x} = \frac{6 x - 2}{x}$

Step 1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

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

Step 2

Subtract $6 x$ from both sides of the equation.

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

Step 3

Add $2$ to both sides of the equation.

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

Step 4

Combine the opposite terms in $3 x^{2} - 2 - 6 x + 2$ .

Add $- 2$ and $2$ .

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

Add $3 x^{2} - 6 x$ and $0$ .

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

Step 5

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

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

$3 x (x) - 6 x = 0$

Factor $3 x$ out of $- 6 x$ .

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

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

$3 x (x - 2) = 0$

Step 6

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

$x = 0$

$x - 2 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 9

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

$x = 0, 2$

Step 10

Exclude the solutions that do not make $\frac{3 x^{2} - 2}{x} = \frac{6 x - 2}{x}$ true.

$x = 2$