3n^2+3n+2=8

Solution for 3n^2+3n+2=8 equation:

Simplifying
3n2 + 3n + 2 = 8

Reorder the terms:
2 + 3n + 3n2 = 8

Solving
2 + 3n + 3n2 = 8

Solving for variable 'n'.

Reorder the terms:
2 + -8 + 3n + 3n2 = 8 + -8

Combine like terms: 2 + -8 = -6
-6 + 3n + 3n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-6 + 3n + 3n2 = 0

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

Factor a trinomial.
3((-2 + -1n)(1 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-2, 1}