3n^2+6n-1=8

Solution for 3n^2+6n-1=8 equation:

Simplifying
3n2 + 6n + -1 = 8

Reorder the terms:
-1 + 6n + 3n2 = 8

Solving
-1 + 6n + 3n2 = 8

Solving for variable 'n'.

Reorder the terms:
-1 + -8 + 6n + 3n2 = 8 + -8

Combine like terms: -1 + -8 = -9
-9 + 6n + 3n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-9 + 6n + 3n2 = 0

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

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

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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 = {-3, 1}