1.) 10n^2 - 35 = 65n
10n^2 - 65n - 35 = 0
2n^2 - 13n - 7 = 0
2n^2 + n - 14n - 7 = 0
n(2n + 1) - 7(2n + 1) = 0
(n - 7)(2n + 1) = 0
n - 7 = 0 or 2n + 1 = 0
n = 7 or n = -1/2
2.) 3x^2 - 8x = 16
3x^2 - 8x - 16 = 0
3x^2 - 12x + 4x - 16 = 0
3x(x - 4) + 4(x - 4)
(3x + 4)(x - 4)
3x + 4 = 0 or x - 4 = 0
x = -4/3 or x = 4
3.) 16n^2 - 114n = -14
16n^2 - 114n + 14 = 0
8n^2 - 57n + 7 = 0
8n^2 - 56n - n + 7 = 0
8n(n - 7) - 1(n - 7) = 0
(8n - 1)(n - 7) = 0
8n - 1 = 0 or n - 7 = 0
n = 1/8 or n = 7
4.) 28n^2 = -96 - 184n
28n^2 + 184n + 96 = 0
7n^2 + 46n + 24 = 0
7n^2 + 42n + 4n + 24 = 0
7n(n + 6) + 4(n + 6) = 0
(7n + 4)(n + 6) = 0
7n + 4 = 0 or n + 6 = 0
n = -4/7 or n = -6
