Solve for n 2n^2=10n+48

$2 n^{2} = 10 n + 48$

Step 1

Subtract $10 n$ from both sides of the equation.

$2 n^{2} - 10 n = 48$

Step 2

Subtract $48$ from both sides of the equation.

$2 n^{2} - 10 n - 48 = 0$

Step 3

Factor the left side of the equation.

Factor $2$ out of $2 n^{2} - 10 n - 48$ .

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

$2 (n^{2}) - 10 n - 48 = 0$

Factor $2$ out of $- 10 n$ .

$2 (n^{2}) + 2 (- 5 n) - 48 = 0$

Factor $2$ out of $- 48$ .

$2 n^{2} + 2 (- 5 n) + 2 \cdot - 24 = 0$

Factor $2$ out of $2 n^{2} + 2 (- 5 n)$ .

$2 (n^{2} - 5 n) + 2 \cdot - 24 = 0$

Factor $2$ out of $2 (n^{2} - 5 n) + 2 \cdot - 24$ .

$2 (n^{2} - 5 n - 24) = 0$

Factor.

Factor $n^{2} - 5 n - 24$ 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 $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$2 ((n - 8) (n + 3)) = 0$

Remove unnecessary parentheses.

$2 (n - 8) (n + 3) = 0$

Step 4

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

$n - 8 = 0$

$n + 3 = 0$

Step 5

Set $n - 8$ equal to $0$ and solve for $n$ .

Set $n - 8$ equal to $0$ .

$n - 8 = 0$

Add $8$ to both sides of the equation.

$n = 8$

Step 6

Set $n + 3$ equal to $0$ and solve for $n$ .

Set $n + 3$ equal to $0$ .

$n + 3 = 0$

Subtract $3$ from both sides of the equation.

$n = - 3$

Step 7

The final solution is all the values that make $2 (n - 8) (n + 3) = 0$ true.

$n = 8, - 3$

Solve for n 2n^2=10n+48

Related Questions

Support LCMGCF.com by disabling your adblocker.