Solve for x 2x^2=2x+12

$2 x^{2} = 2 x + 12$

Step 1

Subtract $2 x$ from both sides of the equation.

$2 x^{2} - 2 x = 12$

Step 2

Subtract $12$ from both sides of the equation.

$2 x^{2} - 2 x - 12 = 0$

Step 3

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} - 2 x - 12$ .

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

$2 (x^{2}) - 2 x - 12 = 0$

Factor $2$ out of $- 2 x$ .

$2 (x^{2}) + 2 (- x) - 12 = 0$

Factor $2$ out of $- 12$ .

$2 (x^{2}) + 2 (- x) + 2 (- 6) = 0$

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

$2 (x^{2} - x) + 2 (- 6) = 0$

Factor $2$ out of $2 (x^{2} - x) + 2 (- 6)$ .

$2 (x^{2} - x - 6) = 0$

Factor.

Factor $x^{2} - x - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Step 4

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

$x - 3 = 0$

$x + 2 = 0$

Step 5

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 6

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

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

$x = 3, - 2$

Solve for x 2x^2=2x+12

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