Solve for x 2x^2=x+3

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

Subtract $x$ from both sides of the equation.

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

Subtract $3$ from both sides of the equation.

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

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 1$ .

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

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

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

$x + 1 = 0$

$2 x - 3 = 0$

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.

$x = - 1$

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

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

$2 x - 3 = 0$

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

Add $3$ to both sides of the equation.

$2 x = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1, 1.5$

Mixed Number Form:

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

Solve for x 2x^2=x+3

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