Solve for x 3x^2=2+x

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

Step 1

Subtract $x$ from both sides of the equation.

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

Step 2

Subtract $2$ from both sides of the equation.

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

Step 3

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $- 1$ as $2$ plus $- 3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

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

Step 4

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

$3 x + 2 = 0$

$x - 1 = 0$

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 $x$ .

Subtract $2$ from 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 $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

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

$x = - \frac{2}{3}, 1$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}, 1$

Decimal Form:

$x = - 0.\overline{6}, 1$

Solve for x 3x^2=2+x

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