Solve by Factoring 2x^2+12x=32

$2 x^{2} + 12 x = 32$

Step 1

Subtract $32$ from both sides of the equation.

$2 x^{2} + 12 x - 32 = 0$

Step 2

Factor $2$ out of $2 x^{2} + 12 x - 32$ .

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

$2 (x^{2}) + 12 x - 32 = 0$

Factor $2$ out of $12 x$ .

$2 (x^{2}) + 2 (6 x) - 32 = 0$

Factor $2$ out of $- 32$ .

$2 x^{2} + 2 (6 x) + 2 \cdot - 16 = 0$

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

$2 (x^{2} + 6 x) + 2 \cdot - 16 = 0$

Factor $2$ out of $2 (x^{2} + 6 x) + 2 \cdot - 16$ .

$2 (x^{2} + 6 x - 16) = 0$

Step 3

Factor.

Factor $x^{2} + 6 x - 16$ 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 $- 16$ and whose sum is $6$ .

$- 2, 8$

Write the factored form using these integers.

$2 ((x - 2) (x + 8)) = 0$

Remove unnecessary parentheses.

$2 (x - 2) (x + 8) = 0$

Step 4

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

$x - 2 = 0$

$x + 8 = 0$

Step 5

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 6

Set $x + 8$ equal to $0$ and solve for $x$ .

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 7

The final solution is all the values that make $2 (x - 2) (x + 8) = 0$ true.

$x = 2, - 8$

Solve by Factoring 2x^2+12x=32

Related Questions

Support LCMGCF.com by disabling your adblocker.