2n^2-6n+6=8

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

Simplifying
2n2 + -6n + 6 = 8

Reorder the terms:
6 + -6n + 2n2 = 8

Solving
6 + -6n + 2n2 = 8

Solving for variable 'n'.

Reorder the terms:
6 + -8 + -6n + 2n2 = 8 + -8

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

Combine like terms: 8 + -8 = 0
-2 + -6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3n + n2)' equal to zero and attempt to solve:

Simplifying
-1 + -3n + n2 = 0

Solving
-1 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + -3n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n + n2 = 0 + 1
-3n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3n + n2 = 1

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 1 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3n + n2 = 3.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(n + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
n + -1.5 = 1.802775638

Simplifying
n + -1.5 = 1.802775638

Reorder the terms:
-1.5 + n = 1.802775638

Solving
-1.5 + n = 1.802775638

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 1.802775638 + 1.5
n = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
n = 3.302775638

Simplifying
n = 3.302775638

Subproblem 2
n + -1.5 = -1.802775638

Simplifying
n + -1.5 = -1.802775638

Reorder the terms:
-1.5 + n = -1.802775638

Solving
-1.5 + n = -1.802775638

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -1.802775638 + 1.5
n = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
n = -0.302775638

Simplifying
n = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.302775638, -0.302775638}
Solution
n = {3.302775638, -0.302775638}