Solve by Factoring n^2+7n+15=5

$n^{2} + 7 n + 15 = 5$

Step 1

Subtract $5$ from both sides of the equation.

$n^{2} + 7 n + 15 - 5 = 0$

Step 2

Subtract $5$ from $15$ .

$n^{2} + 7 n + 10 = 0$

Step 3

Factor $n^{2} + 7 n + 10$ 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 $10$ and whose sum is $7$ .

$2, 5$

Write the factored form using these integers.

$(n + 2) (n + 5) = 0$

Step 4

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

$n + 2 = 0$

$n + 5 = 0$

Step 5

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

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

$n + 2 = 0$

Subtract $2$ from both sides of the equation.

$n = - 2$

Step 6

Set $n + 5$ equal to $0$ and solve for $n$ .

Set $n + 5$ equal to $0$ .

$n + 5 = 0$

Subtract $5$ from both sides of the equation.

$n = - 5$

Step 7

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

$n = - 2, - 5$

Solve by Factoring n^2+7n+15=5

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