Solve by Factoring -4n^2+6n-16=-5n^2

$- 4 n^{2} + 6 n - 16 = - 5 n^{2}$

Add $5 n^{2}$ to both sides of the equation.

$- 4 n^{2} + 6 n - 16 + 5 n^{2} = 0$

Add $- 4 n^{2}$ and $5 n^{2}$ .

$n^{2} + 6 n - 16 = 0$

Factor $n^{2} + 6 n - 16$ 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 $- 16$ and whose sum is $6$ .

$- 2, 8$

Write the factored form using these integers.

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

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

$n - 2 = 0$

$n + 8 = 0$

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

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

$n - 2 = 0$

Add $2$ to both sides of the equation.

$n = 2$

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

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

$n + 8 = 0$

Subtract $8$ from both sides of the equation.

$n = - 8$

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

$n = 2, - 8$

Solve by Factoring -4n^2+6n-16=-5n^2

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