Solve for x 3x^3-x^2=x^2

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

Step 1

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

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

Subtract $x^{2}$ from $- x^{2}$ .

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

Step 2

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

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

$x^{2} (3 x) - 2 x^{2} = 0$

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

$x^{2} (3 x) + x^{2} \cdot - 2 = 0$

Factor $x^{2}$ out of $x^{2} (3 x) + x^{2} \cdot - 2$ .

$x^{2} (3 x - 2) = 0$

Step 3

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

$x^{2} = 0$

$3 x - 2 = 0$

Step 4

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 5

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

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

$3 x - 2 = 0$

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

Add $2$ to both sides of the equation.

$3 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0, 0.\overline{6}$

Solve for x 3x^3-x^2=x^2

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