Solve by Factoring 2x^2+14x-120=0

$2 x^{2} + 14 x - 120 = 0$

Step 1

Factor $2$ out of $2 x^{2} + 14 x - 120$ .

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

$2 (x^{2}) + 14 x - 120 = 0$

Factor $2$ out of $14 x$ .

$2 (x^{2}) + 2 (7 x) - 120 = 0$

Factor $2$ out of $- 120$ .

$2 x^{2} + 2 (7 x) + 2 \cdot - 60 = 0$

Factor $2$ out of $2 x^{2} + 2 (7 x)$ .

$2 (x^{2} + 7 x) + 2 \cdot - 60 = 0$

Factor $2$ out of $2 (x^{2} + 7 x) + 2 \cdot - 60$ .

$2 (x^{2} + 7 x - 60) = 0$

Step 2

Factor.

Factor $x^{2} + 7 x - 60$ 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 $- 60$ and whose sum is $7$ .

$- 5, 12$

Write the factored form using these integers.

$2 ((x - 5) (x + 12)) = 0$

Remove unnecessary parentheses.

$2 (x - 5) (x + 12) = 0$

Step 3

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

$x - 5 = 0$

$x + 12 = 0$

Step 4

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 5

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 6

The final solution is all the values that make $2 (x - 5) (x + 12) = 0$ true.

$x = 5, - 12$

Solve by Factoring 2x^2+14x-120=0

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