Solve for n n^2-14n=-45

$n^{2} - 14 n = - 45$

Add $45$ to both sides of the equation.

$n^{2} - 14 n + 45 = 0$

Factor $n^{2} - 14 n + 45$ 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 $45$ and whose sum is $- 14$ .

$- 9, - 5$

Write the factored form using these integers.

$(n - 9) (n - 5) = 0$

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

$n - 9 = 0$

$n - 5 = 0$

Set $n - 9$ equal to $0$ and solve for $n$ .

Set $n - 9$ equal to $0$ .

$n - 9 = 0$

Add $9$ to both sides of the equation.

$n = 9$

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

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

$n - 5 = 0$

Add $5$ to both sides of the equation.

$n = 5$

The final solution is all the values that make $(n - 9) (n - 5) = 0$ true.

$n = 9, 5$

Solve for n n^2-14n=-45

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