3n^2-6n-82=-10

Solution for 3n^2-6n-82=-10 equation:

Simplifying
3n2 + -6n + -82 = -10

Reorder the terms:
-82 + -6n + 3n2 = -10

Solving
-82 + -6n + 3n2 = -10

Solving for variable 'n'.

Reorder the terms:
-82 + 10 + -6n + 3n2 = -10 + 10

Combine like terms: -82 + 10 = -72
-72 + -6n + 3n2 = -10 + 10

Combine like terms: -10 + 10 = 0
-72 + -6n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2n + n2) = 0

Factor a trinomial.
3((-4 + -1n)(6 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-4, 6}