8n^2+6n-1224=0

Solution for 8n^2+6n-1224=0 equation:

Simplifying
8n2 + 6n + -1224 = 0

Reorder the terms:
-1224 + 6n + 8n2 = 0

Solving
-1224 + 6n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-612 + 3n + 4n2) = 0

Factor a trinomial.
2((-51 + -4n)(12 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-51 + -4n)' equal to zero and attempt to solve:

Simplifying
-51 + -4n = 0

Solving
-51 + -4n = 0

Move all terms containing n to the left, all other terms to the right.

Add '51' to each side of the equation.
-51 + 51 + -4n = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -4n = 0 + 51
-4n = 0 + 51

Combine like terms: 0 + 51 = 51
-4n = 51

Divide each side by '-4'.
n = -12.75

Simplifying
n = -12.75
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-12.75, 12}