Solve by Factoring 6n^2-18n-18=6

$6 n^{2} - 18 n - 18 = 6$

Step 1

Subtract $6$ from both sides of the equation.

$6 n^{2} - 18 n - 18 - 6 = 0$

Step 2

Subtract $6$ from $- 18$ .

$6 n^{2} - 18 n - 24 = 0$

Step 3

Factor $6$ out of $6 n^{2} - 18 n - 24$ .

Factor $6$ out of $6 n^{2}$ .

$6 (n^{2}) - 18 n - 24 = 0$

Factor $6$ out of $- 18 n$ .

$6 (n^{2}) + 6 (- 3 n) - 24 = 0$

Factor $6$ out of $- 24$ .

$6 n^{2} + 6 (- 3 n) + 6 \cdot - 4 = 0$

Factor $6$ out of $6 n^{2} + 6 (- 3 n)$ .

$6 (n^{2} - 3 n) + 6 \cdot - 4 = 0$

Factor $6$ out of $6 (n^{2} - 3 n) + 6 \cdot - 4$ .

$6 (n^{2} - 3 n - 4) = 0$

Step 4

Factor.

Factor $n^{2} - 3 n - 4$ 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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Write the factored form using these integers.

$6 ((n - 4) (n + 1)) = 0$

Remove unnecessary parentheses.

$6 (n - 4) (n + 1) = 0$

Step 5

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

$n - 4 = 0$

$n + 1 = 0$

Step 6

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 7

Set $n + 1$ equal to $0$ and solve for $n$ .

Set $n + 1$ equal to $0$ .

$n + 1 = 0$

Subtract $1$ from both sides of the equation.

$n = - 1$

Step 8

The final solution is all the values that make $6 (n - 4) (n + 1) = 0$ true.

$n = 4, - 1$

Solve by Factoring 6n^2-18n-18=6

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