Solve for n n^2+2n-24=0

$n^{2} + 2 n - 24 = 0$

Step 1

Factor $n^{2} + 2 n - 24$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Write the factored form using these integers.

$(n - 4) (n + 6) = 0$

Step 2

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

$n - 4 = 0$

$n + 6 = 0$

Step 3

Set $n - 4$ equal to $0$ and solve for $n$ .

Set $n - 4$ equal to $0$ .

$n - 4 = 0$

Add $4$ to both sides of the equation.

$n = 4$

Step 4

Set $n + 6$ equal to $0$ and solve for $n$ .

Set $n + 6$ equal to $0$ .

$n + 6 = 0$

Subtract $6$ from both sides of the equation.

$n = - 6$

Step 5

The final solution is all the values that make $(n - 4) (n + 6) = 0$ true.

$n = 4, - 6$

Solve for n n^2+2n-24=0

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