Factor the tirinomals completly then solve. Look for GCF first 15n^2-27n-3=3 and -2x^2-28x-96=0

Question

Can anyone please help me on this ?? I need the answer quick

Answer 1

15n² - 27n - 3 = 3

15n2 - 27n - 6 = 0

3(5n² - 9n - 2) = 0

3(5n + 1)(n - 2) = 0

 

5n + 1 = 0

5n = -1

n = -1/5

 

n - 2 = 0

n = 2

 

Check:

15 * (-1/5)² -27 * -1/5 - 3 = 3

15 * 1/25 + 27/5 - 3 = 3

15/25 + 27/5 - 3 = 3

3/5 + 27/5 - 3 = 3

30/5 - 3 = 3

6 - 3 = 3

3 = 3

 

15 * 2² - 27 * 2 - 3 = 3

15 * 4 - 54 - 3 = 3

60 - 54 - 3 = 3

6 - 3 = 3

3 = 3

 

Problem 2:

-2x² - 28x - 96 = 0

-2(x² + 14x + 48) = 0

-2(x + 8)(x + 6)

 

x + 8 = 0

x = -8

x + 6 = 0

x = -6

 

Checking:

-2 * -8² - 28 * -8 - 96 = 0

-128 + 224 - 96 = 0

-128 + 128 = 0

0 = 0

 

-2 * -6² - 28 * -6 - 96 = 0

-72 + 168 - 96 = 0

-72 + 72 = 0

0 = 0