Solve for x 1=3x^2+2x

$1 = 3 x^{2} + 2 x$

Rewrite the equation as $3 x^{2} + 2 x = 1$ .

$3 x^{2} + 2 x = 1$

Subtract $1$ from both sides of the equation.

$3 x^{2} + 2 x - 1 = 0$

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 $a \cdot c = 3 \cdot - 1 = - 3$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

$3 x^{2} + 2 (x) - 1 = 0$

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

$3 x^{2} + (- 1 + 3) x - 1 = 0$

Apply the distributive property.

$3 x^{2} - 1 x + 3 x - 1 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 1 x) + 3 x - 1 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

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

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

$3 x - 1 = 0$

$x + 1 = 0$

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 $x$ .

Add $1$ to 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 $1$ .

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

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}, - 1$

Solve for x 1=3x^2+2x

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